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20242026
most citedLiftability and vanishing theorems for Fano threefolds in positive characteristic II

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math.AG2026

Frobenius splitting for Fano threefolds

Hiromu Tanaka

We prove that every smooth Fano threefold of characteristic p>5 is quasi-F-split. Moreover, if p>11, then it is F-split.

math.AG2026

105 families of Fano threefolds in positive characteristic

Hiromu Tanaka

Over an algebraically closed field of characteristic , we prove that smooth Fano threefolds form 105 irreducible deformation families.

math.AG2026

Prime Fano threefolds in positive characteristic

Akihiro Kanemitsu, Hiromu Tanaka

We prove that every prime Fano threefold of genus in positive characteristic is a linear section of a Mukai variety.

math.AG2026

Mukai bundles and Brill-Noether generality for prime Fano threefolds in positive characteristic

Hiromu Tanaka

Let be a prime Fano threefold of genus in positive characteristic. For every nontrivial decomposition , we prove that there exists a unique Mukai bundle on …

math.AG2026

Mumford vanishing for threefolds in positive characteristic

Tatsuro Kawakami, Hiromu Tanaka

Let be a projective klt threefold in characteristic and let be a nef Cartier divisor on . We show that for the following two cases: (1) is not…

math.AG2026

Prime Fano threefolds of genus 8 in positive characteristic

Akihiro Kanemitsu, Hiromu Tanaka

We prove that a prime Fano threefold of genus 8 over an algebraically closed field of positive characteristic is isomorphic to a linear section of the Grassmannian variety Gr(2, 6)…