New examples of cylindrical Fano fourfolds

2015/07/07 by Yuri Prokhorov, Mikhail Zaidenberg, Prokhorov, Yuri +1 · 2 citations
Mathematics · #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1507.01748

openalex publication_date 2015/07/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct new families of smooth Fano fourfolds with Picard rank 1, which contain cylinders, i.e., Zariski open subsets of form Z× A¹, where Z is a quasiprojective variety. The affine cones over such a fourfold admit effective G_a-actions. Similar constructions of cylindrical Fano threefolds and fourfolds were done previously in [KPZ11, KPZ14, PZ15].

Citations

• Affine cones over Fano threefolds and additive group actions
• On Contractions of smooth varieties

Cited by

• Prime Fano 4-folds with semi-free torus actions
• Affine cones over Fano-Mukai fourfolds of genus 10 are flexible

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