Extending symmetric determinantal quartic surfaces

2009/09/30 by Stephen Coughlan, Coughlan, Stephen
Mathematics · #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.0909.5547

openalex publication_date 2009/09/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give an explicit construction for the extension of a symmetric determinantal quartic K3 surface to a Fano 6-fold. Remarkably, the moduli of the 6-fold extension are in one-to-one correspondence with the moduli of the quartic surface. As a consequence, we determine a 16-parameter family of surfaces of general type with p_g=1 and K²=2 as weighted complete intersections inside Fano 6-folds.

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