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Local Cohomology, Second Edition by R. Y. Sharp, M. P. Brodmann

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15

Links with projective varieties

One of the reasons for the interest in graded local cohomology is provided by the numerous applications to projective algebraic geometry. This short chapter is intended to provide a little geometric insight, with the aim of motivating the work on Castelnuovo regularity in Chapter 16.

In 2.3.2, we saw that the ideal transform has a geometric meaning in certain cases: if V is an affine variety over K, an algebraically closed field, images is a non-zero ideal of images(V), and U denotes the open subset of V determined by , then ...

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