Deformation of $F$-injectivity and local cohomology
Jun Horiuchi, Lance Edward Miller, Kazuma Shimomoto
TL;DR
This paper establishes conditions under which F-injectivity deforms in algebraic geometry, particularly when the special fiber exhibits isolated CM-locus or F-split properties, enhancing understanding of local cohomology behavior.
Contribution
It provides new sufficient conditions for the deformation of F-injectivity, applicable in geometrically significant scenarios involving CM-locus and F-split fibers.
Findings
F-injectivity deforms under specific conditions
Conditions are satisfied when the special fiber has isolated CM-locus
Conditions are satisfied when the special fiber is F-split
Abstract
We give sufficient conditions for F-injectivity to deform. We show these conditions are met in two common geometrically interesting setting, namely when the special fiber has isolated CM-locus or is F-split.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.