Algebraic Geometry Day

21/10/2020  MCM110

Invited Speakers

Organizers

Conference Schedule

Titles and Abstracts

Penghui Li (Tsinghua University)

Coxeter presentation of character sheaves

The affine Weyl group is generated by simple reflection along faces of an alcove. Categorically, one can reformulate this as the affine Weyl group being a push of finite Weyl groups. We prove an analogous statement that the category of character sheaves is a push out of nilpotent orbital sheaves. As an application, we give a classification of the derived category of character sheaves. This work is partially joint with David Nadler.

Yucheng Liu (Peking University)

Stability conditions on product varieties

Motivated by Douglas's work on D-branes and \PI-stability, Bridgeland introduced a general theory of stability conditions on triangulated categories. In general, stability conditions are very difficult to construct: while we have a very good knowledge in the case of curves and surfaces, starting from 3-folds, no example was known on varieties of general type or Calabi-Yau varieties in dimension 4 or higher. In this talk, I will present a construction of stability conditions on D^b(Coh(XxC)) from a stability condition on D^b(Coh(X)).

Zhiyu Tian (Peking University)

Zero cycles, integral Hodge conjecture, Kato homology, and MMP

I will explain my recent work about zero cycles on rationally connected varieties defined over a Laurent fields and its relation with an integral version of the Hodge conjecture for degenerations of smooth rationally connected varieties. I will also explain how this work fits into a much more general project to study the homology of a Gersten type complex defined by Kato and Bloch-Ogus, where the minimal model program (MMP) makes its appearance.

Zhixian Zhu (Capital Normal University)

Generation of jets on toric varieties

Jet ampleness of line bundles generalizes very ampleness by requiring the existence of enough global sections to separate not just points and tangent vectors, but also their higher order analogues called jets. We give sharp bounds guaranteeing that a line bundle on a projective toric variety is k-jet ample in terms of its intersection numbers with the invariant curves,in terms of the lattice lengths of the edges of its polytope and in terms of the higher concavity of its piecewise linear function.  As an application, we prove the k-jet generalizations of Fujita’s conjectures on toric varieties with arbitrary singularities.