Enumerating odd-degree hyperelliptic curves and abelian surfaces over $\mathbb{P}^1$
Algebraic Geometry
2023-05-09 v6 Algebraic Topology
Number Theory
Abstract
Given asymptotic counts in number theory, a question of Venkatesh asks what is the topological nature of lower order terms. We consider the arithmetic aspect of the inertia stack of an algebraic stack over finite fields to partially answer this question. Subsequently, we acquire new sharp enumerations on quasi-admissible odd-degree hyperelliptic curves over ordered by bounded discriminant height.
Cite
@article{arxiv.2002.00563,
title = {Enumerating odd-degree hyperelliptic curves and abelian surfaces over $\mathbb{P}^1$},
author = {Changho Han and Jun-Yong Park},
journal= {arXiv preprint arXiv:2002.00563},
year = {2023}
}
Comments
40 pages, expository changes and added the arithmetic geometry of inertia stacks of algebraic stacks. Comments welcome!