Mathematical Research Letters

Volume 15 (2008)

Number 2

Some observations on local and projective hypersurfaces

Pages: 207 – 219

DOI: http://dx.doi.org/10.4310/MRL.2008.v15.n2.a1

Author

Hailong Dao (University of Utah)

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 Jothilingam. 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 intersections of subvarieties and cohomological criteria for splitting of vector bundles are discussed.

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