Some observations on local and projective hypersurfaces

2007/01/30 by Hailong Dao, Dao, Hailong
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

paper · pdf · doi:10.48550/arxiv.math/0701881

openalex publication_date 2007/01/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let R be a hypersurface in an equicharacteristic or unramified regular local ring. For a pair of modules (M,N) over R we study applications of rigidity of \Tor^R(M,N), based on ideas by Huneke, Wiegand and Jorgensen. We then focus on the hypersurfaces with isolated singularity and even dimension, and show that modules over such rings behave very much like those over regular local rings. Connections and applications to projective hypersurfaces such as intersection dimension of subvarieties and cohomological criterion for splitting of vector bundles are discussed.

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