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Workshop on algebraic surfaces


Venue: Leibniz Universität Hannover, Main building (Welfenschloss), room f309

Dates: September 15/16, 2016


Miguel Ángel Barja (UPC Barcelona)
Simon Brandhorst (Hannover)
Shigeyuki Kondo (Nagoya)
Martí Lahoz (Jussieu)
Gebhard Martin (TU München)
Tetsuji Shioda (Rikkyo)
Olivier Wittenberg (ENS Paris)



10:00-11:00   Kondo
11:30-12:30   Martin
14:00-15:00   Barja
15:30-16:30   Brandhorst
17:00-18:00   Lahoz


10:00-11:00   Wittenberg
11:30-12:30   Shioda

Titles and abstracts

Linear systems on irregular varieties (Barja)

I will introduce two new invariants associated to a linear system on an irregular variety: the eventual degree and the continuous rank function. From the properties of these invariants I will deduce new higher dimensional Clifford-Severi and Castelnuovo inequalities and will be able to study the limit cases. This is a joint work with Rita Pardini and Lidia Stoppino.


Minimal Salem numbers on supersingular K3 surfaces (Brandhorst)

The entropy of a surface automorphism is either zero or the logarithm of a Salem number, that is an algebraic  integer a>1 which is conjugate to 1/a and all whose other conjugates lie on the unit circle. In the case of a complex K3 surface McMullen gave a strategy to decide whether a given Salem number arises in this way. It combines methods from linear programming, number fields, lattice theory and the Torelli theorems. In  this talk we extend these methods to automorphisms of supersingular K3 surfaces using the crystalline Torelli  theorems and apply them in the case of characteristic 5.
This is joint work with Víctor González Alonso.


On Enriques surfaces with finite automorphism group in characteristic 2 (Kondo)

I will discuss on classification of Enriques surfaces with finite group of automorphisms
in characteristic 2.  In particular I will give an example(s) of such Enriques surfaces whose
canonical covering is a non-normal surface.  This is a joint work with Toshiyuki Katsura.


Bridgeland stability for semiorthogonal decompositions (Lahoz)

This is joint work in progress with Arend Bayer, Emanuele Macrì, and Paolo Stellari. We introduce a new method to induce bounded t-structures on semiorthogonal decompositions. In particular, it allows us to construct Bridgeland stability conditions on the Kuznetsov component of the derived category of (some) Fano threefolds and of cubic fourfolds. To keep connected with the topic of the workshop I will focus in the case of the Kuznetsov component of cubic fourfolds which admits an interpretation as polarized non-commutative K3 surfaces in the sense of Kontsevich-Soibelman.


Enriques surfaces with finite automorphism group in positive (odd) characteristic (Martin)

Enriques surfaces with finite automorphism group over the complex numbers have been classified explicitely by S. Kondo (1986) and in terms of their root invariants by V.V. Nikulin (1983). Using an approach similar to that of S. Kondo, I will explain how to obtain the same classification if the characteristic of the algebraically closed base field is big enough. If time permits, I will also talk about non-existence of certain types of Enriques surfaces with finite automorphism group in smaller characteristics.


Excellent families of elliptic surfaces and Brieskorn's resolution (Shioda)


On the integral Hodge conjecture for real threefolds (Wittenberg)

It is well known that the Hodge conjecture, for complex algebraic
varieties, fails when formulated with integral, rather than rational,
coefficents.  With integral coefficients, it is nevertheless a plausible
statement in the case of curves on varieties whose geometry is simple
enough.  In this talk, I will discuss an analogue for real algebraic
varieties.  This analogue turns out to be closely connected to classical
properties: existence of a curve of even genus, algebraicity of the
homology of the real locus.  This is joint work with Olivier Benoist.


Víctor Gonzalez Alonso
Matthias Schütt


DFG Research training group 1463 'Analysis, geometry and string theory'
Riemann Center for Geometry and Physics
ERC Starting Grant 279723 (SURFARI)