PreprintarXiv licencearXiv
A Murphy's law for supports of forgetful maps between moduli spaces of stable pointed curves
Abstract
We study in this note the decomposition theorem for forgetful maps between moduli spaces of genus g stable pointed curves ℳ̅g,m→ ℳ̅g,n. We prove that as m goes to infinity, every stratum closure in ℳ̅g,n appears as the support of a direct summand in the decomposition theorem. The proof uses Hassett's moduli spaces of stable weighted pointed curves and a wall-crossing argument.
Related
- Finiteness of algebraic Weil-Petersson totally geodesic curves in pointed moduli spaces
- On Euler's abelian relation of the web induced by the forgetful maps on the moduli space ℳ0,n+3: the case when n is even
- Derived category of moduli of pointed curves: II
- Cetraro lectures on integrable systems and moduli spaces of curves
- Birational maps of moduli spaces of stable sheaves on a K3 surface induced by Fourier-Mukai transforms
BibTeX
@misc{zhang2026murphys,
title = {{A Murphy's law for supports of forgetful maps between moduli spaces of stable pointed curves}},
author = {Hao Zhang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.10461},
eprint = {2608.10461},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.10461},
}
RIS
TY - UNPB
TI - A Murphy's law for supports of forgetful maps between moduli spaces of stable pointed curves
AU - Hao Zhang
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2608.10461
UR - https://arxiv.org/abs/2608.10461
AB - We study in this note the decomposition theorem for forgetful maps between moduli spaces of genus g stable pointed curves ℳ̅_g,m→ ℳ̅_g,n. We prove that as m goes to infinity, every stratum closure in ℳ̅_g,n appears as the support of a direct summand in the decomposition theorem. The proof uses Hassett's moduli spaces of stable weighted pointed curves and a wall-crossing argument.
ER -