Return to site

6th Meeting


Meng Chen (Fudan)

On minimal 3-folds of general type with maximal pluricanonical section index
Let X be a minimal 3-fold of general type. The pluricanonical section index $\delta(X)$ is defined to be the minimal integer m so that $P_m(X) \geq 2$. According to J. A. Chen and M. Chen, one has either $1 \leq \delta(X) \leq 15$ or $\delta(X) = 18$. In this talk, we explain further study on the case $\delta(X) = 18$. A direct corollary is that the 57th canonical map of every minimal 3-fold of general type is stably birational, which improves known results.

Lei Fu (Nankai)

Rigidity of $\ell$-adic sheaves
Let X be a smooth connected algebraic curve over an algebraically closed field k, let S be a finite closed subset in X, and let F be a lisse $\ell$-adic sheaf on X - S. We study the deformation of F. By studying the generic fiber of the universal deformation space, we prove a conjecture of Katz which says that if F is irreducible and physically rigid, then F has rigidity index 2.

Yuchen Liu (Princeton)

The volume of Kähler-Einstein Q-Fano varieties
A complex projective variety is Q-Fano if it has klt singularities and the anti-canonical divisor is Q-Cartier and ample. Starting from dimension 2, the anti-canonical volume of a Q-Fano variety can be arbitrarily large, e.g. weighted projective spaces. Recently, Fujita showed that an n-dimensional Kähler-Einstein Q-Fano variety has volume at most (n + 1)n. In this talk, I will discuss a refinement of Fujita’s volume upper bounds involving invariants of the local singularities. If time permits, I will also talk about an equivalent relation between K-semistability and de Fernex-Ein-Mustata type inequalities. Part of this work is joint with Chi Li.

All Posts

Almost done…

We just sent you an email. Please click the link in the email to confirm your subscription!

OKSubscriptions powered by Strikingly