PreprintCC BY 4.0arXiv
Openness of local properties in flat families of superschemes
Abstract
Recently, Jankowski introduced the Serre criteria for superschemes to define the super versions of normality and reducedness (called generic fermionic regularity and reducedness). We show that for a flat, proper morphism f:X→ Y, where X is a superscheme and Y is a Dedekind scheme of finite type over a field of characteristic $0$, the set of y∈ Y for which the fibers Xy are normal, GFRR, regular, and Cohen-Macaulay is open in Y. In particular, if one has a degeneration over 𝔸ℂ1|0, this shows that these properties can be lifted from the special fiber to the generic one.
Related
- Langlands-Shahidi gamma factors and local transfer in families
- Failure of local equi-Lipschitzness for families of Lorentz distances to Cauchy surface foliations
- Geometric Invariant Theory for Affine Superschemes
- Pin Equivariance and Local Dirac Boundary Problems on the Flat Mobius Band
- Flat connections on moduli spaces I: Local (1,0)-extension of the DHS connection
BibTeX
@misc{ahmad2026openness,
title = {{Openness of local properties in flat families of superschemes}},
author = {Ibrahim Ahmad},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.11287},
eprint = {2609.11287},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.11287},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Openness of local properties in flat families of superschemes
AU - Ibrahim Ahmad
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.11287
UR - https://arxiv.org/abs/2609.11287
AB - Recently, Jankowski introduced the Serre criteria for superschemes to define the super versions of normality and reducedness (called generic fermionic regularity and reducedness). We show that for a flat, proper morphism f:X→ Y, where X is a superscheme and Y is a Dedekind scheme of finite type over a field of characteristic $0$, the set of y∈ Y for which the fibers X_y are normal, GFRR, regular, and Cohen-Macaulay is open in Y. In particular, if one has a degeneration over 𝔸_ℂ^1|0, this shows that these properties can be lifted from the special fiber to the generic one.
ER -