Enumerative geometry, Fredholm analysis and moduli spaces of surfaces of general type

Simon Donaldson (Imperial College London and Simons Center for Geometry and Physics)

02-Feb-2021, 15:00-16:00 (3 years ago)

Abstract: In the first part of the talk we will review some background in deformation theory, comparing the points of view from algebraic geometric and differential geometry/global analysis. We will review in outline some known established examples in which a "virtual fundamental class" of a moduli space can be defined. In the second part of the talk we will explore the possibility that these ideas can be applied to moduli spaces of surfaces of general type using the KSBA compactification. We will make some standard observations about these moduli spaces, whose dimension often differs from the virtual dimension. We will illustrate the discussion by a calculation in the case of sextic surfaces with a particular finite symmetry group.

algebraic geometry

Audience: researchers in the topic


ZAG (Zoom Algebraic Geometry) seminar

Series comments: Description: ZAG seminar

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Organizers: Jesus Martinez Garcia*, Ivan Cheltsov*, Jungkai Chen, Jérémy Blanc, Ernesto Lupercio, Yuji Odaka, Zsolt Patakfalvi, Julius Ross, Cristiano Spotti, Chenyang Xu
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