Let V be closed subscheme of [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /] defined by a homogeneous ideal IA = K[X1, . . . , Xn], and let X be the (n - 1)-fold obtained by blowing-up [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="02i" /] along V. If one embeds X in some projective space, one is led to consider the subalgebra K[(Ie)c] of A for some positive integers c and e. The aim of this paper is to study ring-theoretic properties of K[(Ie)c]; this is achieved by developing a theory which enables us to describe the local cohomology of certain modules over generalized Segre products of bigraded algebras. These results are applied to the study of the Cohen-Macaulay property of the homogeneous coordinate ring of the blow-up of the projective space along a complete intersection. We also study the Koszul property of diagonal subalgebras of bigraded standard k-algebras.


Additional Information

Print ISSN
pp. 859-901
Launched on MUSE
Open Access
Back To Top

This website uses cookies to ensure you get the best experience on our website. Without cookies your experience may not be seamless.