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Fano threefolds in positive characteristic II

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arxiv 2308.08122 v5 pith:6FM35MKG submitted 2023-08-16 math.AG

Hiromu Tanaka This is my paper · ORCID
classification math.AG
keywords fanocharacteristicpositivesmoothalgebraicallyalongampleassume
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abstract

Let $X$ be a smooth Fano threefold over an algebraically closed field of positive characteristic. Assume that $|-K_X|$ is very ample and each of the index and the Picard number is equal to one. We prove that $3 \leq g \leq 12$ and $g \neq 11$ for the genus $g$ of $X$. Moreover, we show that there exists no smooth curve on $X$ along which the blowup is Fano.

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  1. Mukai models of Fano varieties

    math.AG 2025-01 conditional novelty 8.0 of 10

    Every Fano variety of dimension at least 3 with Picard number one, genus 6, 7, 8, 9, 10, or 12, and mild singularities is an iterated cone over a transverse linear section of a Mukai variety, with a quadric intersecti...

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