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Wolfgang Ebeling


Institute of Algebraic Geometry
room: g316

phone:+49 511 762-2248
fax:+49 511 762-5803
mail:ebelingmath.uni-hannover.de
homepage:http://www2.iag.uni-hannover.de/~ebeling
hours:Donnerstags: 11:00 - 12:00 Uhr

Bild von  Wolfgang Ebeling

Forschungsgebiete: Algebraische Geometrie, Differentialtopologie, Singularitäten

Teaching

WS 2012/13:

Algebraische Geometrie

Übung zur algebraischen Geometrie

Seminar Symmetriegruppen der Platonischen Körper

Oberseminar zur algebraischen Geometrie und Arithmetischen Geometrie

For further Information please use the Stud.IP

Curriculum Vitae

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Publications


Papers

W. Ebeling (2017): Homological mirror symmetry for singularities, Representation 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 (2017): A note on distinguished bases of singularities, to appear in:  Proceedings of the 14th International Workshop on Real and Complex Singularities, special issue of Topology and its Applications
arXiv: 1611.06074

W. Ebeling, S. M. Gusein-Zade  (2017): Enhanced equivariant Saito duality, to appear in:  J. Algebra Appl.
arXiv: 1506.05604

W. Ebeling, S. M. Gusein-Zade (2017): Higher-order spectra, equivariant Hodge-Deligne polynomials and Macdonald-type equations, Singularities and Computer Algebra (W. Decker et al., eds.), Springer-Verlag 2017, pp. 97-108
arXiv: 1507.08088

W. Ebeling, S. M. Gusein-Zade (2017): Orbifold Milnor lattice and orbifold intersection form, Manuscripta Math.
DOI: 10.1007/s00229-017-0945-4
arXiv: 1607.08740

W. Ebeling, S. M. Gusein-Zade (2017): An algebraic formula for the index of a 1-form on a real quotient singularity
arXiv: 1708.09219

W. Ebeling, S. M. Gusein-Zade (2017): Orbifold zeta functions for dual invertible polynomials, Proc. Edinburgh Math. Soc., Volume 60, Issue 1, 99--106
DOI: 10.1017/S0013091516000043
arXiv: 1407.0154

W. Ebeling, S.M. Gusein-Zade (2017): An equivariant version of the Euler obstruction, Bull. 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 singularities , Arnold 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 polynomials, J. 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 numbers, Topology 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-forms, European 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 numbers, Rev. Mat. Complut. 27 (2014), no. 2, 447–460
DOI: 10.1007/s13163-013-0139-x
arXiv: 1305.6268

W. Ebeling, A. Takahashi (2013): Mirror symmetry between orbifold curves and cusp singularities with group action, Int. Math. Res. Not. IMRN 2013 (2013), no. 10, 2240–2270
DOI: 10.1093/imrn/rns115
arXiv: 1103.5367

W. Ebeling, A. Takahashi (2013): Variance of the exponents of orbifold Landau-Ginzburg models, Math. Res. Lett. 20 (2013), no.01, 51--65
arXiv: 1203.3947

W. Ebeling, D. Ploog (2013): A geometric construction of Coxeter-Dynkin diagrams of bimodal singularities, Manuscripta Math. 140 (2013), no. 1-2, 195–212
arXiv: 1102.5024

W. Ebeling, S. M. Gusein-Zade (2012): Orbifold Euler characteristics for dual invertible polynomials, Mosc. Math. J. 12 (2012), no. 1, 49-54
arXiv: 1107.5542

W. Ebeling, S. M. Gusein-Zade (2012): Equivariant Poincaré series and monodromy zeta functions of quasihomogeneous polynomials, Publ. RIMS Kyoto Univ. 48 (2012), 653-660
arXiv: 1106.1284

W. Ebeling, S. M. Gusein-Zade (2012): Saito duality between Burnside rings for invertible polynomials, Bull. London Math. Soc. 44 (2012), 814-822
arXiv: 1105.1964

W. Ebeling, S. M. Gusein-Zade (2012): On a Newton filtration for functions on a curve singularity, Journal of Singularities 4 (2012), 180-187 more
arXiv: 1206.0135

W. Ebeling, A. Takahashi (2011): Strange duality of weighted homogeneous polynomials, Compos. Math. 147 (2011), 1413-1433.
arXiv: 1003.1590

W. Ebeling, S. M. Gusein-Zade (2011): On divisorial filtrations associated with Newton diagrams, Journal of Singularities 3 (2011), 1-7 more
arXiv: 1008.4659

W. Ebeling, S. M. Gusein-Zade (2011): Monodromy of dual invertible polynomials, Mosc. Math. J. 11 (2011), no. 3, 463-472.
arXiv: 1008.4021

W. Ebeling, D. Ploog (2010): Poincaré series and Coxeter functors for Fuchsian singularities, Adv. Math. 225 (2010), 1387-1398.
arXiv: 0903.4692

W. Ebeling, D. Ploog (2010): McKay correspondence for the Poincaré series of Kleinian and Fuchsian singularities, Math. Ann. 347 (2010), 689-702.
arXiv: 0809.2738

W. Ebeling, S. M. Gusein-Zade (2010): Multi-variable Poincaré series associated with Newton diagrams, Journal of Singularities 1 (2010), 60-68 more
arXiv: 0906.0081

R.-O. Buchweitz, W. Ebeling, H.-Ch. Graf v. Bothmer (2009): Low-dimensional Singularities with Free Divisors as Discriminants, J. Algebraic Geom. 18 (2009), 371-406
arXiv: math.AG/0612119

W. Ebeling (2009): Poincaré series and monodromy of the simple and unimodal boundary singularities, Proc. Steklov Inst. Math. 267 (2009), 50-58
arXiv: 0807.4839

W. Ebeling, S. M. Gusein-Zade (2009): On indices of 1-forms on determinantal singularities, Proc. 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 singularity, Annales 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-forms, In: 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 monodromy, In: 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

W. Ebeling, S. M. Gusein-Zade (2007): Chern obstructions for collections of 1-forms on singular varieties, In: 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): Monodromy, In: 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 (2006): Mirror symmetry, Kobayashi`s duality, and Saito`s duality, Kodai Math. J. 29 (2006), 319-336
arXiv: math.AG/0507134

W. Ebeling, S. Gusein-Zade (2006): Indices of vector fields and 1-forms on singular varieties, In: 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): Quadratic forms for a 1-form on an isolated complete intersection singularity, Math. Z. 252 (2006), 755-766.
arXiv: math.AG/0503336

W. Ebeling, S. M. Gusein-Zade (2006): A filtration defined by arcs on a variety, Uspekhi Mat. Nauk, 61 (2006), no. 2, 163-164 (Russian), (Engl. translation in Russian Math. Surveys 61 (2006), no. 2, 353-355).
arXiv: math/0303331

W. Ebeling, S. M. Gusein-Zade (2005): Radial index and Euler obstruction of a 1-form on a singular variety, Geometriae Dedicata 113, 231--241 (2005)
arXiv: math/0402388

W. Ebeling, S. M. Gusein-Zade (2005): On the arc filtration for the singularities of Arnold`s lists, Math. 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 numbers, Bull. London Math. Soc. 37, 747-754 (2005)
arXiv: math/0303330

W. Ebeling, S. M. Gusein-Zade (2004): Monodromies and Poincaré series of quasihomogeneous complete intersections, Abh. Math. Sem. Univ. Hamburg 74 (2004), 175-179, Preprint 2003  | file |

W. Ebeling, S. M. Gusein-Zade (2004): On indices of meromorphic 1-forms, Compositio Math. 140 (2004), 809-817  | file |

W. Ebeling, S. M. Gusein-Zade, J. Seade (2004): Homological index for 1-forms and a Milnor number for isolated singularities, Int. J. Math. 15, No. 9, (2004) 895--905
arXiv: math/0307239

W. Ebeling (2003): The Poincaré series of some special quasihomogeneous surface singularities, Res. 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 singularity, Mosc. Math. J. 3 (2003), 439-455

W. Ebeling (2002): Poincaré series and monodromy of a two-dimensional quasihomogeneous hypersurface singularity, Manuscripta math. 107, 271-282 (2002)

W. Ebeling, S. M. Gusein-Zade (2002): Poincaré series and zeta function of the monodromy of a quasihomogeneous singularity, Math. Res. Lett. 9 (2002), 509-513  | file |

W. Ebeling, S. M. Gusein-Zade (2001): On the index of a holomorphic 1-form on an isolated complete intersection singularity, Doklady Akad. Nauk 380, 458-461 (2001)

W. Ebeling (2000): Strange duality and polar duality, J. London Math. Soc. (2) 61, 823-834 (2000)

W. Ebeling (1999): Strange duality, mirror symmetry, and the Leech lattice, Singularity theory (Liverpool, 1996), xv–xvi, 55–77, London Math. Soc. Lecture Note Ser., 263, Cambridge Univ. Press, Cambridge, 1999.

W. Ebeling (1999): Lattices and codes, Methods 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 singularity, In: 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. Vassiliev, In: 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 singularities, J. Alg. Geom. 7, 55-76 (1998)

W. Ebeling, S.M. Gusein-Zade (1998): Suspensions of fat points and their intersection forms, In: 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 singularities, J. Math. Sci. 82, 3657-3664 (1996)

W. Ebeling, S. M. Gusein-Zade (1996): Coxeter-Dynkin diagrams of fat points in C2 and of their stabilizations, Math. 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 surfaces, Compositio Math. 91, 277-304 (1994)

W. Ebeling, Ch. Okonek (1991): On the diffeomorphism groups of certain algebraic surfaces, Enseign. Math. 37, 249-262 (1991)

W. Ebeling (1990): An example of two homeomorphic, nondiffeomorphic complete intersection surfaces, Invent. math. 99, 651-654 (1990)

W. Ebeling, Ch. Okonek (1990): Donaldson invariants, monodromy groups and singularities, Internat. J. of Math. 1, 233-250 (1990)

W. Ebeling (1987): Vanishing lattices and monodromy groups of isolated complete intersection singularities, Invent. math. 90, 653-668 (1987)

W. Ebeling (1986): The Milnor lattices of the elliptic hypersurface singularities, Proc. London Math. Soc. (3), 53, 85-111, (1986)

W. Ebeling, C.T.C. Wall (1985): Kodaira singularities and an extension of Arnold's strange duality, Compositio Math. 56, 3-77 (1985)

W. Ebeling (1984): An arithmetic characterisation of the symmetric monodromy groups of singularities, Invent. math. 77, 85-99 (1984)

W. Ebeling (1983): Milnor lattices and geometric bases of some special singularities, In: 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 singularities, Proc. Sympos. Pure Math. (AMS) Vol. 40, Part 1, 327-336 (1983)

W. Ebeling (1983): Arithmetic monodromy groups, Math. Ann. 264, 241-255 (1983)

W. Ebeling (1981): Quadratische Formen und Monodromiegruppen von Singularitäten, Math. Ann. 255, 463-498 (1981)

Expository papers

W. Ebeling, A. Frühbis-Krüger, K. Hulek  (2008): Robuste Silberscheiben, Unimagazin, Leibniz Universität Hannover, 1-2/2008, 36-39

K. Hulek, W. Ebeling (2006): Die Entstehung der Infinitesimalrechnung und der Prioritätsstreit mit Newton, Unimagazin, Leibniz Universität Hannover, 3-4/2006, 46-49

W. Ebeling (2006): Von wegen rund, Unimagazin, Leibniz Universität Hannover, 1-2/2006, 68-70

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

Books

W. Ebeling (2013): Lattices and Codes (3rd Edition), A Course partially based on lectures by Friedrich Hirzebruch, Springer Spektrum 2013 more

W. Ebeling (2007): Functions of Several Complex Variables and Their Singularities , Graduate Studies in Mathematics, Vol. 83. American Mathematical Society, Providence, RI, 2007. more

W. Ebeling (2001): Funktionentheorie, Differentialtopologie und Singularitäten, Vieweg Wiesbaden Braunschweig, 2001 more

W. Ebeling (1987): The Monodromy Groups of Isolated Singularities of Complete Intersections, Lecture Notes in Mathematics, Vol. 1293, Springer Verlag, Berlin Heidelberg New York London Paris Tokyo, 1987

Edited books

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