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SUMMARY:Zhe Xu (Simon Fraser University)
DTSTART:20221013T223000Z
DTEND:20221013T233000Z
DTSTAMP:20260422T054103Z
UID:SFUQNTAG/72
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/SFUQNTAG/72/
 ">On the local behaviour of symmetric differentials on the blow-up of Du V
 al singularities</a>\nby Zhe Xu (Simon Fraser University) as part of SFU N
 T-AG seminar\n\nLecture held in K-9509.\n\nAbstract\nDu Val singularities 
 appear in the classification of algebraic surfaces and other areas of alge
 braic geometry. Wahl's concept of local Euler characteristics of sheaves h
 elps in describing the properties of these singularities. We consider the 
 sheaf of symmetric differentials and compute one ingredient of the local E
 uler characteristic: the codimension of those symmetric differentials that
  extend to the blow-up of the singularity in the space of those that are r
 egular around it. For singularities of type \\(A_n\\)\, we show that this 
 codimension can be expressed combinatorially as a lattice point count in a
  polytope. Ehrhart's quasi-polynomials allow us to find closed expressions
  for this codimension as a function of the symmetric differential degree. 
 We expect our method to generalize to all Du Val singularities.\n
LOCATION:https://researchseminars.org/talk/SFUQNTAG/72/
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