Description
Commutative algebra seminar
Time: 22 Nov, Thursday, 11am-12noon.
Venue: Ramanujan Hall.
Speaker : Tony J. Puthenpurakal.
Title: On p_g ideals.
Abstract: Let $(A,\m)$ be an excellent normal domain of dimension two.
We define an $\m$-primary ideal $I$ to be a $p_g$-ideal if the Rees algebra
$A[It]$ is a \CM \ normal domain. When $A$ contains an algebraically
closed field $k \cong A/\m$ then Okuma, Watanabe and Yoshida proved that
$A$ has
$p_g$-ideals and furthermore product of two $p_g$-ideals is a $p_g$ ideal.
In this talk we show that if $A$ is an excellent normal domain of
dimension two containing a field $k \cong A/\m$ of characteristic zero
then also $A$ as $p_g$-ideals. Furthermore product of two $p_g$-ideals is
$p_g$.