Beijing Algebraic Geometry Day
Home page  http://www.jliumath.com/conferences/2024BAGDI.html  
Address  Academy of Mathematics and Systems Science @ N202 (second floor of the South Building)  
Time  2024.09.23 (Monday)  
Schedule 


Abstract 
We study mutually onepoint incident 22 planes in a smooth cubic 4fold in char. 2, and cubic 4folds with 11 cusps in char. 3.
(1) Such 22 planes (resp. 11 cusps) appear for every cubic 4fold associated with supersingular K3 surface in char. 2 (resp. in char. 3 with Artin invariant at most 6).
(2) They are Fermat and Klein type and have an action of the Mathieu groups M22 and M11, respectively, in the most special case of Artin invarinat 1.
We prove the Kuznetsov components of a series of hypersurface in projective space reconstruct the hypersurfaces. Our method allows us
to work for hypersurfaces of weighted projective space, and obtain the reconstruction theorem of veronese double cone, which is a
longtime opening case. I will show how to construct infinitesimal variation of Hodge structure from certain Kuznetsov components.
Using classical generic Torelli theorem, this implies Kuznetsov components reconstruct the algebraic variety generically. Joint
with J. Rennemo and ShiZhuo Zhang.
Deuring gave a now classical formula for the number of supersingular elliptic curves in characteristic \(p\). We generalize this to a formula
for the cycle class of the supersingular locus in the moduli space of principally polarized abelian varieties of given dimension \(g\) in
chacteristic \(p\). The formula determines the class up to a multiple and shows that it lies in the tautological ring. We also give the
multiple for \(g\) up to \(4\). This is joint work with S. Harashita.
Moduli spaces of stable sheaves on Fano threefolds are known to exhibit pathological behavior in general.
Meanwhile, for certain specific cases—such as ideal sheaves of curves with small degree and genus in the cubic threefold,
or moduli spaces of lowerrank aCM bundles—these spaces are wellbehaved.
From a modern derived categorical perspective, we have the socalled Kuznetsov component \(\text{Ku}(X)\) in \(D(X)\). The wellbehaved moduli spaces mentioned above actually parametrize stable objects within \(\text{Ku}(X)\). In this talk, I will begin by recapping this framework with a detailed overview of known results. I will then present our recent work on higherdimensional moduli spaces of stable objects in \(\text{Ku}(X)\). This is a joint work with Yingbang Lin, Laura Pertusi, and Xiaolei Zhao.
There are two basic objects in projective algebraic geometry: one is a variety of minimal degree and the other is a del Pezzo variety.
In this talk, I'd like to introduce higher secant varieties of minimal degree and del Pezzo higher secant varieties to nonexpert with
modest backgrounds. Recently, classification and characterization of such varieties have been paid attention. I will also give many
interesting examples explaining main results.


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