On support varieties for modules over complete intersections

Bergh, Petter

doi:10.1090/S0002-9939-07-09009-0

On support varieties for modules over complete intersections
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by Petter Andreas Bergh PDF

Proc. Amer. Math. Soc. 135 (2007), 3795-3803 Request permission

Abstract:

Let $(A, \mathfrak {m}, k)$ be a complete intersection of codimension $c$, and let $\tilde {k}$ be the algebraic closure of $k$. We show that every homogeneous algebraic subset of $\tilde {k}^c$ is the cohomological support variety of an $A$-module, and that the projective variety of a complete indecomposable maximal Cohen–Macaulay $A$-module is connected.

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