(The seminar webpage is here.)
Sam Grushevsky (Stony Brook University)
September 29, 2017
Geometry of compactified moduli of cubic threefolds
Starting from considering the GIT compactification of the moduli of cubic threefolds, the “wonderful” compactification, which is smooth with normal crossing boundary, is constructed by an explicit sequence of blowups. We show that there exists a family of intermediate jacobians over the wonderful compactification. We compute the cohomology of the wonderful compactification by comparing it to the symplectic resolution. Based on joint works with Casalaina-Martin, Hulek, Laza
Felix Janda (University of Michigan)
October 6, 2017
Genus two curves on quintic threefolds
Virtual (Gromov-Witten) counts of maps from algebraic curves to quintic 3-folds in projective space have been of significant interest for mathematicians and physicists since the early 90s. While there are (very inefficient) algorithms for computing any specific Gromov-Witten invariant, explicit formulae are only known in genus zero and one. On the other hand, physicists have explicit conjectural formulas up to genus 51.
I will discuss a new approach to the Gromov-Witten theory of the quintic (using logarithmic geometry) which yields an explicit formula in genus two that agrees with the physicists’ conjecture.
Remy van Dobben de Bruyn (Columbia)
October 20, 2017
Dominating varieties by liftable ones
Given a smooth projective variety over an algebraically closed field of positive characteristic, can we always dominate it by another smooth projective variety that lifts to characteristic 0? We give a negative answer to this question.