First neighborhood complete ideals in two-dimensional Muhly local domains are projectively full

Debremaeker, Raymond

doi:10.1090/S0002-9939-08-09735-9

First neighborhood complete ideals in two-dimensional Muhly local domains are projectively full
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Proc. Amer. Math. Soc. 137 (2009), 1649-1656 Request permission

Abstract:

Let $(R, \mathcal {M})$ be a two-dimensional Muhly local domain, i.e., an integrally closed Noetherian local domain with algebraically closed residue field and the associated graded ring an integrally closed domain.

Motivated by recent work of Ciuperca, Heinzer, Ratliff and Rush on projectively full ideals, we prove that every complete ideal adjacent to the maximal ideal $\mathcal {M}$ is projectively full.

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