Generic vanishing theory in positive characteristic

Jefferson Baudin

doi:10.4171/lem/1106

July 16, 2026L’Enseignement MathématiqueOpen Access

Generic vanishing theory in positive characteristic

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Key Points

The aim is to simplify and enhance the fundamental theorems of generic vanishing theory in positive characteristic.
Improved proofs of fundamental theorems regarding effective vanishing of differentials in varieties.
Analysis of properties related to the Albanese dimension and normal proper varieties.
Demonstrated H^{0}(X, ω_{X}) ≠ 0 for normal proper varieties of maximal Albanese dimension.
Concluded S^{0}(X, ω_{X}) ≠ 0 when the Albanese variety is ordinary.

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Implication

Simplifies generic vanishing theory, demonstrating results in varieties of positive characteristic.

Abstract

We simplify and improve the main fundamental theorems of positive characteristic generic vanishing theory. As a quick corollary of the theory, we prove that a normal proper variety X of maximal Albanese dimension satisfies H⁰(X, ωX) ≠ 0 . If Alb(X) is in addition ordinary, then S⁰(X, ωX) ≠ 0 .

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Jefferson Baudin (2026) studied this question.

synapsesocial.com/papers/6a5c6874118b92953e3ed1fc https://doi.org/10.4171/lem/1106

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Generic vanishing theory in positive characteristic

Key Points

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Implication

Abstract

Discussion

Cite This Study

Generic vanishing theory in positive characteristic

Key Points

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Implication

Abstract

Discussion

Cite This Study

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