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Torelli Theorem for moduli stacks of vector bundles on tame Deligne Mumford curves
Abstract
We prove a Torelli theorem for full moduli stacks of vector bundles of rank at least three with fixed determinant on a smooth, proper, geometrically connected, tame Deligne--Mumford curve of coarse genus at least two over an arbitrary field k. We also prove a Torelli theorem for the full moduli stack of vector bundles of rank at least three of fixed-degree under an explicit compatibility hypothesis. The method is intrinsic to the stack: faithful special-linear linearizations recover Picard stacks, and determinants of tangent complexes recover the canonical principal polarization. This is the first part in a series of two papers.
Related
- Torelli theorem for the product of moduli spaces of vector bundles over a curve
- Torelli theorem for the moduli spaces of twisted vector bundles on smooth projective curves
- Existence of coarse moduli superspaces for Deligne--Mumford superstacks
- Irregular Hodge Bundles for Deligne--Mumford Landau--Ginzburg Families with Fixed Pole Orders
- Equivariant principal bundles over toric Deligne--Mumford stacks
BibTeX
@misc{ghosh2026torelli,
title = {{Torelli Theorem for moduli stacks of vector bundles on tame Deligne Mumford curves}},
author = {Soham Ghosh and Ting Gong and Max Lieblich},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.29011},
eprint = {2609.29011},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.29011},
}
RIS
TY - UNPB
TI - Torelli Theorem for moduli stacks of vector bundles on tame Deligne Mumford curves
AU - Soham Ghosh
AU - Ting Gong
AU - Max Lieblich
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2609.29011
UR - https://arxiv.org/abs/2609.29011
AB - We prove a Torelli theorem for full moduli stacks of vector bundles of rank at least three with fixed determinant on a smooth, proper, geometrically connected, tame Deligne--Mumford curve of coarse genus at least two over an arbitrary field k. We also prove a Torelli theorem for the full moduli stack of vector bundles of rank at least three of fixed-degree under an explicit compatibility hypothesis. The method is intrinsic to the stack: faithful special-linear linearizations recover Picard stacks, and determinants of tangent complexes recover the canonical principal polarization. This is the first part in a series of two papers.
ER -