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Vector bundles over elliptic surfaces

Vitantonio Peragine
Institution: 
SISSA
Location: 
A-136
Schedule: 
Wednesday, December 4, 2019 - 16:00
Abstract: 

This will be a review talk about vector bundles on elliptic surfaces. We will start by showing that S-equivalence classes of semistable vector bundles of rank n and trivial determinant over an integral curve E of arithmetic genus 1 (possibly singular) have a coarse moduli space, which is a projective space P of dimension n-1. Then, we will describe two methods for constructing universal families of regular bundles over PxE, one based on the idea of a spectral cover of P, and the other on the universal extension of two suitably chosen vector bundles on E. Finally, we will explain how these ideas can be generalized to the relative context of a family of Weierstrass cubics with a section.

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