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arXiv · 2509.05577

The intrinsic cohomology ring of the universal compactified Jacobian over the moduli space of stable curves

Younghan Bae·Davesh Maulik·Junliang Shen·Qizheng Yin
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Abstract

The purpose of this paper is to study the cohomology rings of universal compactified Jacobians. Over the moduli space $\overline{\mathcal{M}}_{g,n}$ of Deligne-Mumford stable marked curves with $n\geq 1$, on the one hand we show that the cohomology ring of a universal fine compactified Jacobian is sensitive to the choice of a nondegenerate stability condition which answers a question of Pandharipande; on the other hand, we prove that the cohomology ring admits a degeneration via the perverse filtration which is independent of the (nondegenerate) stability condition. The latter defines the intrinsic cohomology ring of the universal compactified Jacobian which only relies on $g,n$. Our main tools include the support theorems, the recently developed Fourier theory for dualizable abelian fibrations, and the universal double ramification cycle relations associated with the universal Picard stack.

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Younghan Bae, Davesh Maulik, Junliang Shen, Qizheng Yin. 2025-10-28. The intrinsic cohomology ring of the universal compactified Jacobian over the moduli space of stable curves. https://arxiv.org/abs/2509.05577

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