Publications of Wolfgang Ebeling

Papers

  • Wolfgang Ebeling, Atsushi Takahashi (2023): Graded matrix factorizations of size two and reductionManuscripta Math. 170, 409-425 (2023)
    DOI: 10.1007/s00229-022-01372-4
    arXiv: 2101.05075
  • Wolfgang Ebeling, Sabir M. Gusein-Zade (2023): Indices of vector fields and 1-formsHandbook of Geometry and Topology of Singularities, Volume IV, Springer, Cham, 2023, 251–305.
    arXiv: 2107.01967
  • Wolfgang Ebeling, Sabir M. Gusein-Zade (2022): Mirror symmetry on levels of non-abelian Landau--Ginzburg orbifoldsJ. Geom. Phys. 179 (2022) 104617
    DOI: 10.1016/j.geomphys.2022.104617
    arXiv: 2204.02069
  • Wolfgang Ebeling, Atsushi Takahashi (2021): Strange duality between the quadrangle complete intersection singularitiesArnold Mathematical Journal 7, 519-540 (2021)
    DOI: 10.1007/s40598-021-00181-z
    arXiv: 2102.08010
  • Wolfgang Ebeling, Sabir M. Gusein-Zade (2021): A version of the Berglund-Hübsch-Henningson duality with non-abelian groupsInt. Math. Res. Not. IMRN 2021, No. 16, 12305-12329 (2021)
    DOI: 10.1093/imrn/rnz167
    arXiv: 1807.04097
  • Wolfgang Ebeling (2020): Distinguished bases and monodromy of complex hypersurface singularitiesHandbook of Geometry and Topology of Singularities I, (J.L. Cisneros Molina et al., eds.) Springer, Cham, 449-490, 2020
    arXiv: 1905.12435
  • Wolfgang Ebeling, Atsushi Takahashi (2020): Lattices for Landau-Ginzburg orbifoldsMath. Z. 296 (2020), 639-659
    DOI: 10.1007/s00209-019-02441-3
    arXiv: 1809.06566
  • Wolfgang Ebeling, Sabir M. Gusein-Zade (2020): Dual invertible polynomials with permutation symmetries and the orbifold Euler characteristicSIGMA 16 (2020), 051, 15 pages
    arXiv: 1907.11421
  • Wolfgang Ebeling, Sabir M. Gusein-Zade (2020): On the orbifold Euler characteristics of dual invertible polynomials with non-abelian symmetry groupsPure Appl. Math. Q. 16, No. 4, 1099-1113, 2020
    arXiv: 1811.05781
  • S.M. Gusein-Zade, W. Ebeling (2018): The index of a 1-form on a real quotient singularity.Funktsional. Anal. i Prilozhen. 52, no. 2, 78-81 (2018) (English translation in Funct. Anal. Appl. 52, no. 2, 144-146 (2018))
  • W. Ebeling, S. M. Gusein-Zade (2018): Enhanced equivariant Saito dualityJ. Algebra Appl. Vol. 17, No. 10 (2018) 1850181
    DOI: 10.1142/S0219498818501815
    arXiv: 1506.05604
  • W. Ebeling, S. M. Gusein-Zade (2018): An algebraic formula for the index of a 1-form on a real quotient singularityMath. Nachrichten 291, 2543-2556 (2018)
    DOI: https://doi.org/10.1002/mana.201700453
    arXiv: 1708.09219
  • W. Ebeling, S. M. Gusein-Zade (2018): Orbifold Milnor lattice and orbifold intersection formManuscripta Math. 155, 335-353 (2018)
    DOI: 10.1007/s00229-017-0945-4
    arXiv: 1607.08740
  • Wolfgang Ebeling (2018): A note on distinguished bases of singularitiesTopology and its Applications 234 (2018), 259-268
    DOI: 10.1016/j.topol.2017.11.015
    arXiv: 1611.06074
  • Wolfgang Ebeling (2018): A McKay correspondence for the Poincar\'e series of some finite subgroups of ${\rm SL}_3(\CC)$Special Volume in honor of the life and mathematics of Egbert Brieskorn, Journal of Singularities 18 (2018), 397-408
    DOI: 10.5427/jsing.2018.18t
    arXiv: 1712.07985
  • W. Ebeling (2017): Homological mirror symmetry for singularitiesRepresentation Theory - Current Trends and Perspectives (H. Krause et al., eds.), EMS Series of Congress Reports, Zürich 2017, pp. 75-107
    arXiv: 1601.06027
  • W. Ebeling, S. M. Gusein-Zade (2017): Orbifold zeta functions for dual invertible polynomialsProc. Edinburgh Math. Soc., Volume 60, Issue 1, 99--106
    DOI: 10.1017/S0013091516000043
    arXiv: 1407.0154
  • W. Ebeling, S. M. Gusein-Zade (2017): Higher-order spectra, equivariant Hodge-Deligne polynomials and Macdonald-type equationsSingularities and Computer Algebra (W. Decker et al., eds.), Springer-Verlag 2017, pp. 97-108
    arXiv: 1507.08088
  • W. Ebeling, S.M. Gusein-Zade (2017): An equivariant version of the Euler obstructionBull. Braz. Math. Soc. (N.S.) 48 (2017), 199-208
    DOI: 10.1007/s00574-016-0022-8
    arXiv: 1407.6587
  • W. Ebeling, A. Takahashi (2016): Strange duality between hypersurface and complete intersection singularitiesArnold Mathematical Journal 2 (2016), 277-298
    DOI: 10.1007/s40598-016-0044-8
    arXiv: 1508.02226
  • W. Ebeling, S. M. Gusein-Zade, A. Takahashi (2016): Orbifold E-functions of dual invertible polynomialsJ. Geom. Phys. 106 (2016), 184-191
    DOI: 10.1016/j.geomphys.2016.03.026
    arXiv: 1509.04101
  • W. Ebeling, S. M. Gusein-Zade (2015): Indices of collections of equivariant 1-forms and characteristic numbersTopology Appl. 191 (2015), 153-162
    DOI: 10.1016/j.topol.2015.06.002
    arXiv: 1406.4278
  • W. Ebeling, S.M. Gusein-Zade (2015): Equivariant indices of vector fields and 1-formsEuropean J. of Math. 1 (2015), 286-301
    DOI: 10.1007/s40879-015-0036-6
    arXiv: 1307.2054
  • W. Ebeling, A. Takahashi (2014): A geometric definition of Gabrielov numbersRev. Mat. Complut. 27 (2014), no. 2, 447–460
    DOI: 10.1007/s13163-013-0139-x
    arXiv: 1305.6268
  • W. Ebeling, A. Takahashi (2013): Variance of the exponents of orbifold Landau-Ginzburg modelsMath. Res. Lett. 20 (2013), no.01, 51--65
    arXiv: 1203.3947
  • W. Ebeling, A. Takahashi (2013): Mirror symmetry between orbifold curves and cusp singularities with group actionInt. Math. Res. Not. IMRN 2013 (2013), no. 10, 2240–2270
    DOI: 10.1093/imrn/rns115
    arXiv: 1103.5367
  • W. Ebeling, D. Ploog (2013): A geometric construction of Coxeter-Dynkin diagrams of bimodal singularitiesManuscripta Math. 140 (2013), no. 1-2, 195–212
    arXiv: 1102.5024
  • W. Ebeling, S. M. Gusein-Zade (2012): Saito duality between Burnside rings for invertible polynomialsBull. London Math. Soc. 44 (2012), 814-822
    arXiv: 1105.1964
  • W. Ebeling, S. M. Gusein-Zade (2012): Equivariant Poincaré series and monodromy zeta functions of quasihomogeneous polynomialsPubl. RIMS Kyoto Univ. 48 (2012), 653-660
    arXiv: 1106.1284
  • W. Ebeling, S. M. Gusein-Zade (2012): Orbifold Euler characteristics for dual invertible polynomialsMosc. Math. J. 12 (2012), no. 1, 49-54
    arXiv: 1107.5542
  • W. Ebeling, S. M. Gusein-Zade (2012): On a Newton filtration for functions on a curve singularityJournal of Singularities 4 (2012), 180-187 More info
    arXiv: 1206.0135
  • W. Ebeling, A. Takahashi (2011): Strange duality of weighted homogeneous polynomialsCompos. Math. 147 (2011), 1413-1433.
    arXiv: 1003.1590
  • W. Ebeling, S. M. Gusein-Zade (2011): Monodromy of dual invertible polynomialsMosc. Math. J. 11 (2011), no. 3, 463-472.
    arXiv: 1008.4021
  • W. Ebeling, S. M. Gusein-Zade (2011): On divisorial filtrations associated with Newton diagramsJournal of Singularities 3 (2011), 1-7 More info
    arXiv: 1008.4659
  • W. Ebeling, D. Ploog (2010): Poincaré series and Coxeter functors for Fuchsian singularitiesAdv. Math. 225 (2010), 1387-1398.
    arXiv: 0903.4692
  • W. Ebeling, D. Ploog (2010): McKay correspondence for the Poincaré series of Kleinian and Fuchsian singularitiesMath. Ann. 347 (2010), 689-702.
    arXiv: 0809.2738
  • W. Ebeling, S. M. Gusein-Zade (2010): Multi-variable Poincaré series associated with Newton diagramsJournal of Singularities 1 (2010), 60-68 More info
    arXiv: 0906.0081
  • R.-O. Buchweitz, W. Ebeling, H.-Ch. Graf v. Bothmer (2009): Low-dimensional Singularities with Free Divisors as DiscriminantsJ. Algebraic Geom. 18 (2009), 371-406
    arXiv: math.AG/0612119
  • W. Ebeling (2009): Poincaré series and monodromy of the simple and unimodal boundary singularitiesProc. Steklov Inst. Math. 267 (2009), 50-58
    arXiv: 0807.4839
  • W. Ebeling, S. M. Gusein-Zade (2009): On indices of 1-forms on determinantal singularitiesProc. Steklov Inst. Math. 267 (2009), 113-124.
    arXiv: 0806.0219
  • H.-Ch. Graf v. Bothmer, W. Ebeling, X. Gomez-Mont (2008): An algebraic formula for the index of a vector field on an isolated complete intersection singularityAnnales de l`Institut Fourier, Vol. 58, no. 5 (2008), 1761-1783
    arXiv: math.AG/0601640
  • W. Ebeling, S. M. Gusein-Zade (2007): Indices of collections of 1-formsIn: Singularities in Geometry and Topology. Proceedings of the Trieste Singularity Summer School and Workshop 2005 (J.-P. Brasselet et al., eds.), World Scientific, Singapore 2007, pp. 629-639
  • W. Ebeling, S. M. Gusein-Zade (2007): Lectures on monodromyIn: Singularities in Geometry and Topology. Proceedings of the Trieste Singularity Summer School and Workshop 2005 (J.-P. Brasselet et al., eds.), World Scientific, Singapore 2007, pp. 234-252
  • Wolfgang Ebeling, Sabir M. Gusein-Zade (2007): Chern obstructions for collections of 1-forms on singular varietiesIn: Singularity Theory. Proceedings of the 2005 Marseille Singularity School and Conference (D. Chéniot et al., eds), World Scientific, Singapore 2007, pp. 557-564
    arXiv: math.AG/0503422
  • W. Ebeling (2006): Mirror symmetry, Kobayashi`s duality, and Saito`s dualityKodai Math. J. 29 (2006), 319-336
    arXiv: math.AG/0507134
  • W. Ebeling (2006): MonodromyIn: Singularities and Computer Algebra (Ch. Lossen, G. Prister, eds.), London Math. Soc. Lecture Note Series 324, Cambridge University Press 2006, 129-155
    arXiv: math.AG/0507171
  • W. Ebeling, S. Gusein-Zade (2006): Indices of vector fields and 1-forms on singular varietiesIn: Global Aspects of Complex Geometry (F. Catanese et al., eds.), Springer-Verlag 2006, 129-169
    arXiv: math.AG/0601439
  • W. Ebeling, S. M. Gusein-Zade (2006): A filtration defined by arcs on a varietyUspekhi Mat. Nauk, 61 (2006), no. 2, 163-164 (Russian), (Engl. translation in Russian Math. Surveys 61 (2006), no. 2, 353-355).
    arXiv: math/0303331
  • Wolfgang. Ebeling, Sabir M. Gusein-Zade (2006): Quadratic forms for a 1-form on an isolated complete intersection singularityMath. Z. 252 (2006), 755-766.
    arXiv: math.AG/0503336
  • W. Ebeling, S. M. Gusein-Zade (2005): On the arc filtration for the singularities of Arnold`s listsMath. Proc. Cambridge Philos. Soc. 138 (2005), 307-314, Preprint 2003
    arXiv: math.AG/0309243
  • W. Ebeling, S. M. Gusein-Zade (2005): Indices of vector fields or 1-forms and characteristic numbersBull. London Math. Soc. 37, 747-754 (2005)
    arXiv: math/0303330
  • Wolfgang Ebeling, Sabir M. Gusein-Zade (2005): Radial index and Euler obstruction of a 1-form on a singular varietyGeometriae Dedicata 113, 231--241 (2005)
    arXiv: math/0402388
  • W. Ebeling, S. M. Gusein-Zade (2004): Monodromies and Poincaré series of quasihomogeneous complete intersectionsAbh. Math. Sem. Univ. Hamburg 74 (2004), 175-179, Preprint 2003 | File |
  • W. Ebeling, S. M. Gusein-Zade (2004): On indices of meromorphic 1-formsCompositio Math. 140 (2004), 809-817
  • W. Ebeling, S. M. Gusein-Zade, J. Seade (2004): Homological index for 1-forms and a Milnor number for isolated singularitiesInt. J. Math. 15, No. 9, (2004) 895--905
    arXiv: math/0307239
  • W. Ebeling (2003): The Poincaré series of some special quasihomogeneous surface singularitiesRes. Inst. Math. Sci. 39 (2003), 393-413
    arXiv: math.AG/0004086
  • W. Ebeling, S. M. Gusein-Zade (2003): Indices of 1-forms on an isolated complete intersection singularityMosc. Math. J. 3 (2003), 439-455
  • W. Ebeling (2002): Poincaré series and monodromy of a two-dimensional quasihomogeneous hypersurface singularityManuscripta math. 107, 271-282 (2002)
  • W. Ebeling, S. M. Gusein-Zade (2002): Poincaré series and zeta function of the monodromy of a quasihomogeneous singularityMath. Res. Lett. 9 (2002), 509-513
  • W. Ebeling, S. M. Gusein-Zade (2001): On the index of a holomorphic 1-form on an isolated complete intersection singularityDoklady Akad. Nauk 380, 458-461 (2001)
  • W. Ebeling (2000): Strange duality and polar dualityJ. London Math. Soc. (2) 61, 823-834 (2000)
  • W. Ebeling (1999): Strange duality, mirror symmetry, and the Leech latticeSingularity theory (Liverpool, 1996), xv–xvi, 55–77, London Math. Soc. Lecture Note Ser., 263, Cambridge Univ. Press, Cambridge, 1999.
  • W. Ebeling (1999): Lattices and codesMethods of discrete mathematics (Braunschweig, 1999), 103–143, Quad. Mat., 5, Dept. Math., Seconda Univ. Napoli, Caserta, 1999
  • W. Ebeling, S. M. Gusein-Zade (1999): On the index of a vector field at an isolated singularityIn: The Arnoldfest: Proceedings of a Conference in Honour of V. I. Arnold for his Sixtieth Birthday (E. Bierstone, B. Khesin, A. Khovanskii, J. Marsden, eds.), Fields Institute Communications 24, Am. Math. Soc., Providence 1999, pp. 141-152
  • W. Ebeling (1998): Appendix to the paper of V.A. VassilievIn: Singularities. The Brieskorn Anniversary Volume (V.I. Arnold, G.-M. Greuel, J.H.M. Steenbrink, eds.), Progr. Math., Vol. 162, Birkhäuser, Basel 1998, 235-237
  • W. Ebeling, J. H. M. Steenbrink (1998): Spectral pairs for isolated complete intersection singularitiesJ. Alg. Geom. 7, 55-76 (1998)
  • W. Ebeling, S.M. Gusein-Zade (1998): Suspensions of fat points and their intersection formsIn: Singularities. The Brieskorn Anniversary Volume (V.I. Arnold, G.-M. Greuel, J.H.M. Steenbrink, eds.), Progr. Math., Vol. 162, Birkhäuser, Basel 1998, 141-165
  • W. Ebeling (1996): On Coxeter-Dynkin diagrams of hypersurface singularitiesJ. Math. Sci. 82, 3657-3664 (1996)
  • W. Ebeling, S. M. Gusein-Zade (1996): Coxeter-Dynkin diagrams of fat points in C2 and of their stabilizationsMath. Ann. 306, 487–512 (1996)
  • W. Ebeling, S. M. Gusein-Zade (1995): Coxeter-Dynkin diagrams of the complete intersection singularities Z_9 and Z_{10}Math. Z. 218, 549-562 (1995)
  • W. Ebeling, Ch. Okonek (1994): Homology Hopf surfacesCompositio Math. 91, 277-304 (1994)
  • W. Ebeling, Ch. Okonek (1991): On the diffeomorphism groups of certain algebraic surfacesEnseign. Math. 37, 249-262 (1991)
  • W. Ebeling, Ch. Okonek (1990): Donaldson invariants, monodromy groups and singularitiesInternat. J. of Math. 1, 233-250 (1990)
  • Wolfgang Ebeling (1990): An example of two homeomorphic, nondiffeomorphic complete intersection surfacesInvent. math. 99, 651-654 (1990)
  • Wolfgang Ebeling (1987): Vanishing lattices and monodromy groups of isolated complete intersection singularitiesInvent. math. 90, 653-668 (1987)
  • Wolfgang Ebeling (1986): The Milnor lattices of the elliptic hypersurface singularitiesProc. London Math. Soc. (3), 53, 85-111, (1986)
  • W. Ebeling, C.T.C. Wall (1985): Kodaira singularities and an extension of Arnold's strange dualityCompositio Math. 56, 3-77 (1985)
  • W. Ebeling (1984): An arithmetic characterisation of the symmetric monodromy groups of singularitiesInvent. math. 77, 85-99 (1984)
  • W. Ebeling (1983): Milnor lattices and geometric bases of some special singularitiesIn: Noæuds, tresses et singularités (Ed. C. Weber), Monographie Enseign. Math. 31, Genàve 1983, 129-146 und Enseign. Math. 29, 263-280 (1983)
  • W. Ebeling (1983): On the monodromy groups of singularitiesProc. Sympos. Pure Math. (AMS) Vol. 40, Part 1, 327-336 (1983)
  • W. Ebeling (1983): Arithmetic monodromy groupsMath. Ann. 264, 241-255 (1983)
  • W. Ebeling (1981): Quadratische Formen und Monodromiegruppen von SingularitätenMath. Ann. 255, 463-498 (1981)

Papers in a research magazine

  • W. Ebeling, A. Frühbis-Krüger, K. Hulek (2008): Robuste SilberscheibenUnimagazin, Leibniz Universität Hannover, 1-2/2008, 36-39
  • K. Hulek, W. Ebeling (2006): Die Entstehung der Infinitesimalrechnung und der Prioritätsstreit mit NewtonUnimagazin, Leibniz Universität Hannover, 3-4/2006, 46-49
  • W. Ebeling (2006): Von wegen rundUnimagazin, Leibniz Universität Hannover, 1-2/2006, 68-70

Expository papers

  • W. Ebeling (2001): 'Horst Tietz Fund'für Oberwolfach aus der Taufe gehobenDMV-Mitteilungen 3, 54-55 (2001)

Edited books

  • W. Ebeling, K. Hulek, K. Smoczyk (2011): Complex and Differential GeometryConference Hannover 2009, Springer Proceedings in Mathematics 8, 2011

Books

  • W. Ebeling (2013): Lattices and Codes (3rd Edition)A Course partially based on lectures by Friedrich Hirzebruch, Springer Spektrum 2013 More info
  • W. Ebeling (2007): Functions of Several Complex Variables and Their SingularitiesGraduate Studies in Mathematics, Vol. 83. American Mathematical Society, Providence, RI, 2007. More info
  • W. Ebeling (2001): Funktionentheorie, Differentialtopologie und SingularitätenVieweg Wiesbaden Braunschweig, 2001 More info
  • W. Ebeling (1987): The Monodromy Groups of Isolated Singularities of Complete IntersectionsLecture Notes in Mathematics, Vol. 1293, Springer Verlag, Berlin Heidelberg New York London Paris Tokyo, 1987