On blow-ups of the quintic del Pezzo 3-fold and varieties of power sums of quartic hypersurfaces

2009/04/23 by Hiromichi Takagi, Takagi, Hiromichi, Francesco Zucconi +1
Computer Science · Mathematics · #14H42 (Secondary) #14J45 (Primary) 14N05 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.0904.3586

openalex publication_date 2009/04/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct new subvarieties in the varieties of power sums for certain quartic hypersurfaces. This provides a generalization of Mukai's description of smooth prime Fano threefolds of genus twelve as the varieties of power sums for plane quartics. In fact, in our second paper, we show that these quartics are exactly the Scorza quartics associated to general pairs of trigonal curves and ineffective theta characteristics and this enables us to prove there the main cojecture of Dolgachev and Kanev.

Related

• Scorza quartics of trigonal spin curves and their varieties of power sums
• Spin curves and Scorza quartics
• Geometry and Algebra of prime Fano 3-folds of genus 12
• Rational quartic curves in the Mukai-Umemura variety
• The topology of terminal quartic 3-folds