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arXiv · 2303.16836

Wall-crossing of universal Brill-Noether classes

Alex Abreu·Nicola Pagani
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Abstract

We give an explicit graph formula, in terms of decorated boundary strata classes, for the wall-crossing of universal Brill-Noether classes. More precisely, fix n>0 and d<g , and two stability conditions \phi^-, \phi^+ for degree d compactified universal (over the moduli space of stable n-pointed curves of genus g) Jacobians that lie on opposite sides of a stability hyperplane. Our main result is a formula for the difference between the Brill-Noether classes, compared via the pullback along the (rational) identity map. The calculation involves constructing a resolution of the identity map by means of subsequent blow-ups.

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Alex Abreu, Nicola Pagani. 2023-03-29. Wall-crossing of universal Brill-Noether classes. https://arxiv.org/abs/2303.16836

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