PreprintarXiv licencearXiv
On the Rank of Normal Functions on Pointed Curves
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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BibTeX
@misc{fassina2026rank,
title = {{On the Rank of Normal Functions on Pointed Curves}},
author = {Lorenzo Fassina},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.22901},
eprint = {2609.22901},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.22901},
}
RIS
TY - UNPB
TI - On the Rank of Normal Functions on Pointed Curves
AU - Lorenzo Fassina
PY - 2026
DA - 2026/09/19
PB - arXiv
DO - 10.48550/arxiv.2609.22901
UR - https://arxiv.org/abs/2609.22901
AB - 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.
ER -