Gorenstein ring of sections and complete intersections in codimension two

Abstract

Let R be a regular local ring of dimension n 5, and p a prime ideal of height 2. Let (V , O V ) be the punctured spectrum of R/p. We show that if the ring Γ (V , O V ) is Gorenstein, then R/p is complete intersection. We also show that an analog of the splitting criterion for vector bundles of small rank on projective spaces given in [N. Mohan Kumar, C. Peterson, A. Prabhakar Rao, Monads on projective spaces, Manuscripta Math. 112 (2003) 183-189; p. 185, Theorem 1] holds for vector bundles of small rank on punctured spectrum of regular local rings.