# Warwick Algebraic Geometry Seminar

### Autumn Term 2018

The Warwick Algebraic Geometry Seminar will be taking place this term on Tuesday afternoons at 2pm in MS.05, unless otherwise stated. We also have a later slot available to us on Tuesdays at 4pm in B3.03, which we may make use of occasionally.

In addition to our own activities, we will also be arranging regular trips to various algebraic geometry activities running in the UK, including the COW seminar, the East Midlands Seminar in Geometry (EmSG), the London Geometry and Topology Seminar, the GLEN seminar, and the British Algebraic Geometry meeting (BrAG).

If you are interested in receiving announcements about upcoming seminars and other algebraic geometry activities at Warwick, you're welcome to join our mailing list. To do this, just send an email to Michel van Garrel (michel (dot) van (hyphen) garrel (at) warwick (dot) ac (dot) uk) and ask to be added to the list.

Week | Date | Speaker | Title |

1 | 2nd October | Christian Böhning | Stable nonrationality of ℚ-Fano threefolds with anticanonical models of small codimension |

2 | 9th October | Fabien Cléry | Vector-valued Siegel modular forms of degree 2 with character |

3 | 15th-17th October | 3CinG meeting | COW on October 16th |

4 | 23rd October | Michel van Garrel | On a conjecture by Voskresenskii |

5 | 29th Oct - 2nd Nov | Workshop at Loughborough | Fano varieties and their automorphisms |

6 | 6th November | Alessio D'Alì | Generalized Stanley-Reisner rings and translative group actions |

7 | 13th November | Mattia Talpo | Topological realization of varieties over ℂ((t)) via log geometry |

8.1 | 20th November | Ehud Meir (2pm in MS.05) | Applications of GIT to Hopf algebras |

8.2 | 20th November | Jeongseok Oh (4pm in B3.03) | Localized Chern characters for 2-periodic complexes |

9 | 27th November | Stefan Schreieder | Stably irrational hypersurfaces of small slopes |

10 | 4th December | René Mboro | Remarks on varieties of essential CH_{0}-dimension at
most 2 |

## Abstracts

**Christian Böhning (Warwick) - Stable nonrationality of ℚ-Fano threefolds with anticanonical models of small codimension**- We report on joint work with Hans-Christian v. Bothmer (still very much in progress) on rationality properties of some classes of ℚ-Fano threefolds given in a Gorenstein format in the sense of Reid et al. Besides proving stable non-rationality for very general members of families of such Fanos in new cases, this provides a unified view on and recovers results of Ahmadinezhad-Okada-Totaro et al. Time permitting, we will in addition say a few words about singular models of cubics in the context of the degeneration method.
**Fabien Cléry (Loughborough) - Vector-valued Siegel modular forms of degree 2 with character**- The link between covariants of binary sextics and vector-valued Siegel modular forms of degree 2, obtained in a previous work with G. van der Geer and C. Faber, is an efficient way for producing such modular forms. By using this link, the structure of some graded rings of vector-valued Siegel modular forms of degree 2 with character will be given. This talk is based on a joint work with G. van der Geer and C. Faber.
**Michel van Garrel (Warwick) - On a conjecture by Voskresenskii**- In this collaboration with M. Florence, we are interested in settings where the notions of rationality and stable rationality become equivalent. We explore this question for tori over any field, where the equivalence of the two notions was conjectured by Voskresenskii. For a certain class of tori, this conjecture was proven by Klyachko by means of general principles. We give a new explicit proof of this result by exhibiting simple morphisms. This proof has an application in cryptography.
**Alessio D'Alì (Warwick) - Generalized Stanley-Reisner rings and translative group actions**- The Stanley-Reisner correspondence, which assigns a commutative ring to each finite simplicial complex, is a useful and well-studied bridge between commutative algebra and combinatorics. In 1987 Sergey Yuzvinsky proposed a construction that allows to see the Stanley-Reisner ring of a finite simplicial complex as the ring of global sections of a sheaf of rings on a poset. Motivated by applications in the theory of Abelian arrangements, Emanuele Delucchi and I extend Yuzvinsky's construction to the case of (possibly infinite) finite-length simplicial posets. This generalization behaves well with respect to quotients of simplicial complexes and posets by translative group actions.
**Mattia Talpo (Imperial) - Topological realization of varieties over ℂ((t)) via log geometry**- I will describe some work in progress with Piotr Achinger about defining a “Betti realization” functor for varieties over the formal punctured disk Spec ℂ((t)), i.e. defined by polynomials with coefficients in the field of formal Laurent series in one variable. Our construction is via “good models” over the power series ring ℂ[[t]] and the “Kato-Nakayama” construction in logarithmic geometry, that I will review during the talk.
**Ehud Meir (Aberdeen) - Applications of GIT to Hopf algebras**- In this talk I will describe applications of Geometric Invariant Theory (GIT) to the study of finite dimensional Hopf algebras and related algebraic structures. If time permits, I will also explain a related classification result in the theory of finite group schemes and a non-commutative geometry generalisation of them, known as Hopf orders.
**Jeongseok Oh (KIAS) - Localized Chern characters for 2-periodic complexes**- For a two-periodic complex of vector bundles, Polishchuk and Vaintrob have constructed its localized Chern character. We explore some basic properties of this localized Chern character. In particular, we show that the cosection localization defined by Kiem and Li is equivalent to a localized Chern character operation for the associated two-periodic Koszul complex, strengthening a work of Chang, Li, and Li. We apply this equivalence to the comparison of virtual classes of moduli of ε-stable quasimaps and moduli of the corresponding LG ε-stable quasimaps. This is based on joint work with Bumsig Kim. Furthermore, if the time is permitted, we discuss the comparison of virtual structure sheaves either. The latter is joint work with B. Sreedhar.
**Stefan Schreieder (LMU München) - Stably irrational hypersurfaces of small slopes**-
We explain the rationality problem for hypersurfaces in projective space and review
what is known about this problem. We then explain how to prove that over any
uncountable field of characteristic different from two, a very general hypersurface of
dimension n > 2 and degree at least 2+log
_{2}(n) is not stably rational. This significantly improves earlier results of Kollár and Totaro. **René Mboro (University of Bonn) - Remarks on varieties of essential CH**_{0}-dimension at most 2-
We present the notion, due to Voisin, of essential
CH
_{0}-dimension of a variety and give two flavors of sufficient conditions for a variety with trivial group of 0-cycles and essential CH_{0}-dimension at most 2 to have, in fact, essential CH_{0}-dimension 0 (i.e. to admit a decomposition of the diagonal).

## Getting Here

Directions to the university may be found here. Once you're on campus, the Mathematics Institute is located in the Zeeman building; you can download a map of the campus here.

Please note that if you are arriving by public transport, the University of Warwick is not in fact in the town of Warwick, or indeed anywhere near it. Instead, it is located a short distance southwest of Coventry. If you are coming by train the closest stations are Coventry and Leamington Spa.

To get to campus from Coventry station you should take bus 11, 11U, or 12X; all three leave from stand ER3 at the bus hub outside the railway station. At the time of writing, a single ticket from Coventry station to the university costs £2.10; a day ticket is £4; an all day group ticket £8; please note that the buses from Coventry only accept exact change.

To get to campus from Leamington Spa station you should take bus U1, U2, or U17. Please note that these buses do not leave from directly outside the station; instead, the nearest bus stop is just around the corner on Victoria Terrace. A map of the route may be found here. At the time of writing, a single ticket from Leamington Spa station to the university costs £2.75.

This page is maintained by Michel van Garrel. Please email comments and corrections to michel (dot) van (hyphen) garrel (at) warwick (dot) ac (dot) uk.

Many thanks to Alan Thompson and Liana Heuberger for designing and updating this page and for allowing its carbon copy to appear here.