Generic vanishing fails for singular varieties and in characteristic p>0
Christopher D Hacon, S\'andor J Kov\'acs
TL;DR
This paper demonstrates that the generic vanishing theorem, which holds in smooth characteristic zero cases, does not extend to singular varieties or positive characteristic fields, highlighting limitations in these contexts.
Contribution
It provides counterexamples showing the failure of generic vanishing in singular and positive characteristic settings, challenging previous assumptions.
Findings
Generic vanishing fails for singular varieties
Counterexamples in characteristic p>0
Limitations of generic vanishing in broader contexts
Abstract
We show that generic vanishing fails for singular varieties and in characteristic p>0.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Intracerebral and Subarachnoid Hemorrhage Research · Advanced Algebra and Geometry