PreprintCC BY 4.0arXiv
Degenerations of shifted symplectic moduli stacks of sheaves
Abstract
Let S be a smooth, affine noetherian ℂ-scheme, and let X/S be a smooth, quasi-projective family of Calabi--Yau d-folds. We prove that the derived moduli stack of flat families of properly supported coherent sheaves on X/S has a relative (2−d)-shifted symplectic structure by generalizing a construction of Brav--Dyckerhoff. The main points are to show that the category IndCoh(X) is a smooth, compact QCoh(S)-module and to identify our moduli stack of interest as a substack of the moduli of pseudo-perfect objects in IndCoh(X). Finally, we discuss two examples of families of smooth, quasi-projective Calabi--Yau threefolds that are potentially useful for applications in enumerative geometry.
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BibTeX
@misc{huynh2026degenerations,
title = {{Degenerations of shifted symplectic moduli stacks of sheaves}},
author = {Matthew Huynh},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.36922},
eprint = {2609.36922},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.36922},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Degenerations of shifted symplectic moduli stacks of sheaves
AU - Matthew Huynh
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.36922
UR - https://arxiv.org/abs/2609.36922
AB - Let S be a smooth, affine noetherian ℂ-scheme, and let X/S be a smooth, quasi-projective family of Calabi--Yau d-folds. We prove that the derived moduli stack of flat families of properly supported coherent sheaves on X/S has a relative (2−d)-shifted symplectic structure by generalizing a construction of Brav--Dyckerhoff. The main points are to show that the category IndCoh(X) is a smooth, compact QCoh(S)-module and to identify our moduli stack of interest as a substack of the moduli of pseudo-perfect objects in IndCoh(X). Finally, we discuss two examples of families of smooth, quasi-projective Calabi--Yau threefolds that are potentially useful for applications in enumerative geometry.
ER -