PreprintCC BY 4.0arXiv
Germwise singular Fourier--Mukai partnerships
Abstract
We study how local behavior on the base controls whether integral transforms induce fully faithful functors or equivalences between singularity categories of proper flat families. By working with étale germs, we show (under mild hypotheses) that the loci where this happens are open and are compatible with étale base change. Moreover, we give examples, exhibit an autoequivalence of the singularity category which detects regularity of the base, and compute these loci for arithmetic families.
Related
- Fourier-Mukai transforms by a family of stable sheaves and preservation of stability
- Birational maps of moduli spaces of stable sheaves on a K3 surface induced by Fourier-Mukai transforms
- Fourier--Mukai loci are open and base change
- Fourier-Mukai partners and autoequivalences of moduli spaces of vector bundles
- A Non Commutative Grauert Theorem and Fourier Mukai Duality for Generalized Complex Tori
BibTeX
@misc{lank2026germwise,
title = {{Germwise singular Fourier--Mukai partnerships}},
author = {Pat Lank},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.29944},
eprint = {2610.29944},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.29944},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Germwise singular Fourier--Mukai partnerships
AU - Pat Lank
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.29944
UR - https://arxiv.org/abs/2610.29944
AB - We study how local behavior on the base controls whether integral transforms induce fully faithful functors or equivalences between singularity categories of proper flat families. By working with étale germs, we show (under mild hypotheses) that the loci where this happens are open and are compatible with étale base change. Moreover, we give examples, exhibit an autoequivalence of the singularity category which detects regularity of the base, and compute these loci for arithmetic families.
ER -