Algebraic Geometry Seminar
Spring 2019 — Tuesdays 3:30  4:30 PM, location LCB 222
Date  Speaker  Title — click for abstract (if available) 
January 8th LCB 225 (Wednesday, special time & place) 
Yuchen Liu Yale 
Discreteness of local volumes
A few years ago, Chi Li introduced the notion of local volume of Kawamata log
terminal (klt) singularities as the minimum normalized volume of valuation. This invariant
carries lots of interesting geometric information of the singularity, for instance: it
characterizes smooth points; it detects orbifold order of quotient singularities; it is
bounded from above by the minimal log discrepancy. In this talk, I will discuss the
conjecture that local volumes of klt singularities in a fixed dimension with finite
coefficient set has only accumulation point zero. We confirm this conjecture when ambient
singularities are bounded. This is a joint work in progress with Jingjun Han and Lu Qi.

January 14th 
Carl Lian Columbia University 
Enumerating pencils with moving ramification on curves
We consider the general problem of enumerating branched covers of the projective line from a fixed general curve subject to ramification conditions at possibly moving points. Our main computations are in genus 1; the theory of limit linear series allows one to reduce to this case. We first obtain a simple formula for a weighted count of pencils on a fixed elliptic curve E, where basepoints are allowed. We then deduce, using an inclusionexclusion procedure, formulas for the numbers of maps E>P^1 with moving ramification conditions. A striking consequence is the invariance of these counts under a certain involution. Our results generalize work of Harris, Logan, Osserman, and FarkasMoschettiNaranjoPirola.

January 21st 


January 28th 


Frebruary 4th 


February 11th 
Ben Wormleighton UC Berkeley 

February 18th 


February 25th 
Kenta Sato RIKEN 
AkizukiNakano vanishing on globally Fsplit 3folds and its application
By Raynaud's result, AkizukiNakano vanishing theorem holds on a smooth globally Fsplit variety if the characteristic is larger than or equal to the dimension.
However, very little is known for singular varieties.
In this talk, we first show a weak form of the AkizukiNakano vanishing theorem on (possibly singular) globally Fsplit 3folds.
As application, we obtain results on deformations for globally Fsplit Fano 3folds.
We also apply it to prove the Kodaira vanishing for thickenings of locally complete intersection globally Fregular 3folds, which is a positive characteristic analogue of a result by BhattBlickleLyubeznikSinghZhang.
This talk is based on joint work with Shunsuke Takagi.

March 3rd 


March 17th 
Alexander Polishchuk University of Oregon 

March 24th 


March 31st 


April 7th 


April 14th 


April 21st 


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