Scorza quartics of trigonal spin curves and their varieties of power sums

2008/01/11 by Hiromichi Takagi, Takagi, Hiromichi, Zucconi, Francesco · 1 citation
Mathematics · #14H42 #14J45 #14N05 #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.0801.1760

openalex publication_date 2008/01/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Our fundamental result is the construction of new subvarieties in the varieties of power sums for the Scorza quartic of any general pairs of trigonal curves and non-effective theta characteristics. This is a generalization of Mukai's description of smooth prime Fano threefolds of genus twelve as the varieties of power sums for plane quartics. Among other applications, we give an affirmative answer to the conjecture of Dolgachev and Kanev on the existence of the Scorza quartic for any general pairs of curves and non-effective theta characteristics.

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• Projective and birational geometry of Grassmannians and other special varieties

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