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arXiv · 2609.22901

On the Rank of Normal Functions on Pointed Curves

Lorenzo Fassina
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Abstract

We study a natural class of normal functions on the moduli space of pointed curves and determine their rank at every point. We prove that the rank is maximal outside the corresponding stratum of Abelian differentials, while along this stratum it drops by exactly one. As a consequence, we describe the local geometry of the associated double ramification locus.

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Lorenzo Fassina. 2026-09-19. On the Rank of Normal Functions on Pointed Curves. https://arxiv.org/abs/2609.22901

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