Geometry of fine compactified Jacobians in genus 1

Giovedì 20 maggio 2021 alle ore 14:30, Orsola Tommasi (Padova) terrà il seminario di Geometria dal titolo "Geometry of fine compactified Jacobians in genus 1".

Abstract
The degree d universal Jacobian parametrizes degree d line bundles on smooth curves. There are several approaches on how to extend it to a proper family over the moduli space of stable curves. In this talk, we introduce a simple definition of a fine compactified universal Jacobian. We focus on the case of genus 1 and obtain a combinatorial classification for fine universal compactified Jacobians, which enables us to construct new examples of them. The description we obtain for universal fine compactified Jacobians of genus 1 also yields a formula for their rational cohomology. This is joint work with Nicola Pagani (Liverpool).

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