Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
173 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Moduli of nodal curves on K3 surfaces (1502.07378v3)

Published 25 Feb 2015 in math.AG

Abstract: We consider modular properties of nodal curves on general $K3$ surfaces. Let $\mathcal{K}p$ be the moduli space of primitively polarized $K3$ surfaces $(S,L)$ of genus $p\geqslant 3$ and $\mathcal{V}{p,m,\delta}\to \mathcal{K}p$ be the universal Severi variety of $\delta$--nodal irreducible curves in $|mL|$ on $(S,L)\in \mathcal{K}_p$. We find conditions on $p, m,\delta$ for the existence of an irreducible component $\mathcal{V}$ of $\mathcal{V}{p,m,\delta}$ on which the moduli map $\psi: \mathcal{V}\to \mathcal{M}_g$ (with $g= m2 (p -1) + 1-\delta$) has generically maximal rank differential. Our results, which for any $p$ leave only finitely many cases unsolved and are optimal for $m\geqslant 5$ (except for very low values of $p$), are summarized in Theorem 1.1 in the introduction.

Summary

We haven't generated a summary for this paper yet.