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Existence of good ideals in 2-dimensional normal Gorenstein rings (COMMA) March 14, 2013 (02:00 PM PDT - 03:00 PM PDT)
Parent Program: --
Location: MSRI: Simons Auditorium
Speaker(s) Kei-ichi Watanabe (Nihon University)
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Let (A,m) be a Noetherian Gorenstein local ring of dimension d. An m-primary ideal of A is called "good" if G(I):=\oplus I^n/I^{n+1} is Gorenstein with a(G) =1-d. Equivalently, if Q is a minimal reduction of I, I is good if and only if I^2=QI and Q:I = I.

In a paper Goto-Iai-Watanabe, Good ideals in Gorenstein local rings, T.A.M.S. 353 (2000), we studied good ideals in 2 dimensional rational singularities. In this talk, we show existence of good ideals for non-rational surface singularities using cohomology groups of anti-nef cycles on a resolution of the singularity.

This is a joint work with Tomohiro Okuma and Ken-ichi Yoshida.

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