Construction of algebraic covers

2017/09/11 by Eduardo Dias, Dias, Eduardo
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #math.AC #math.AG

paper · pdf · doi:10.48550/arxiv.1709.03341

openalex publication_date 2017/09/11 · arxiv created 2020/01/06 · arxiv updated 2020/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let Y be an algebraic variety, F a locally free sheaf of O_Y-modules, and R(F) the O_Y-algebra Sym^\bullet F. In this paper we study local properties of sheaves of O_R(F)-ideals I such that R(F))/I is an algebraic cover of Y. Following the work of Miranda for triple covers, for Q a direct summand of R(F), we say that a morphism Φ\colon Q\rightarrowR(F)/\langleQ⟩ is a covering homomorphism if it induces such an ideal. As an application we study in detail the case of Gorenstein covering maps of degree 6 for which the direct image of φ_*O_X admits an orthogonal decomposition. These are deformation of S₃-Galois branch covers.

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