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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Compactified Universal Jacobians via Geometric Invariant Theory

## Compactified Universal Jacobians via Geometric Invariant TheoryAdd to your list(s) Download to your calendar using vCal - George Cooper (University of Oxford)
- Wednesday 17 January 2024, 12:00-12:45
- Seminar Room 2, Newton Institute.
If you have a question about this talk, please contact nobody. EMG - New equivariant methods in algebraic and differential geometry Associated to any smooth projective curve $C$ is its degree $d$ Jacobian variety, parametrising isomorphism classes of degree $d$ line bundles on $C$. Letting the curve vary as well, one is led to the universal Jacobian stack. This stack admits several compactifications over the stack of marked stable curves $\overline{\mathcal{M}}_{g,n}$, depending on the choice of a stability condition. In this talk I will begin by introducing these compactified universal Jacobians, and explain how their moduli spaces can be constructed using Geometric Invariant Theory (GIT). I will then introduce new analogues of these moduli stacks, where the sheaves being parametrised are of a fixed unstable Harder—Narasimhan type, and explain how non-reductive GIT allows one to prove the existence of quasi-projective moduli spaces for these stacks, which in many cases are naturally projective. This talk is based on arXiv:2210.11457 and upcoming work. This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
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