2020/03/24 by Alexander Kuznetsov, Yuri Prokhorov, Kuznetsov, Alexander +1
Mathematics · Pharmacology, Toxicology and Pharmaceutics · #14E05 #14E08 #14E30 #14J35 #14J40 #14J45 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Alkaloids: synthesis and pharmacology #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2003.10761
openalex publication_date 2020/03/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We discuss birational properties of Mukai varieties, i.e., of higher-dimensional analogues of prime Fano threefolds of genus g ∈ \7,8,9,10\ over an arbitrary field k of zero characteristic. In the case of dimension n ≥ 4 we prove that these varieties are k-rational if and only if they have a k-point except for the case of genus 9, where we assume n ≥ 5. Furthermore, we prove that Mukai varieties of genus g ∈ \7,8,9,10\ and dimension n ≥ 5 contain cylinders if they have a k-point. Finally, we prove that the embedding X \hookrightarrow Gr(3,7) for prime Fano threefolds of genus 12 is defined canonically over any field and use this to give a new proof of the criterion of rationality.