The zeta functions of the Fano surfaces of cubic threefolds

2013/04/15 by Xavier Roulleau, Roulleau, Xavier
Mathematics · #14G10 #14G15 #14J29 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1304.4076

openalex publication_date 2013/04/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give an algorithm to compute the zeta function of the Fano surface of lines of a smooth cubic threefold F into ℙ⁴ defined over a finite field. We obtain some examples of Fano surfaces with supersingular reduction.

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