PreprintarXiv licencearXiv
Alternative moduli of twisted curves
Abstract
We define new Artin stack compactifications of the moduli of smooth curves, which parameterize "relatively polarized curves" consisting of stacky semistable curves equipped with line bundles that are trivialized away from the rational bridges. Using techniques from birational geometry, we prove that stacks of relatively polarized curves admit the classical coarse space M̅g of stable curves as a good moduli space. One of our main motivations is a companion paper where we construct a proper moduli space of SLN-bundles on relatively polarized curves. This suggests the hypothesis that relatively polarized curves are suitable sources for defining Gromov-Witten theory for Artin stack targets.
Related
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BibTeX
@misc{halpernleistner2026alternative,
title = {{Alternative moduli of twisted curves}},
author = {Daniel Halpern-Leistner and Andres Fernandez Herrero and Giovanni Inchiostro and Sara Stephens},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.30069},
eprint = {2610.30069},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.30069},
}
RIS
TY - UNPB
TI - Alternative moduli of twisted curves
AU - Daniel Halpern-Leistner
AU - Andres Fernandez Herrero
AU - Giovanni Inchiostro
AU - Sara Stephens
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.30069
UR - https://arxiv.org/abs/2610.30069
AB - We define new Artin stack compactifications of the moduli of smooth curves, which parameterize "relatively polarized curves" consisting of stacky semistable curves equipped with line bundles that are trivialized away from the rational bridges. Using techniques from birational geometry, we prove that stacks of relatively polarized curves admit the classical coarse space M̅_g of stable curves as a good moduli space. One of our main motivations is a companion paper where we construct a proper moduli space of SL_N-bundles on relatively polarized curves. This suggests the hypothesis that relatively polarized curves are suitable sources for defining Gromov-Witten theory for Artin stack targets.
ER -