We give explicit formulas for the a-invariant of a ring defined by the minors of fixed size of a generic symmetric matrix whose entries are given positive degrees in such a way that all minors are homogeneous. The same result was obtained independently, and with different methods, by A. Conca. In this article the a -invariant is computed more generally for algebras with straightening laws on a doset (DASL) in terms of its principal chains. The precise result is this: Let Π be a semimodular lattice and D a saturated, monotonely graded doset of Π with principal chain P(D) on D over a field k . Then the a-invariant is given by −degP(D) . In preliminary sections we discuss Cohen-Macaulayness of (DASLs), and relate principal chains to "fundamental chains'' which correspond to "fundamental faces'' of simplicial complexes as introduced by Hibi.
The Cohen-Macaulayness and the a-invariant of an algebra with straightening laws on a doset
BARILE, Margherita
1994-01-01
Abstract
We give explicit formulas for the a-invariant of a ring defined by the minors of fixed size of a generic symmetric matrix whose entries are given positive degrees in such a way that all minors are homogeneous. The same result was obtained independently, and with different methods, by A. Conca. In this article the a -invariant is computed more generally for algebras with straightening laws on a doset (DASL) in terms of its principal chains. The precise result is this: Let Π be a semimodular lattice and D a saturated, monotonely graded doset of Π with principal chain P(D) on D over a field k . Then the a-invariant is given by −degP(D) . In preliminary sections we discuss Cohen-Macaulayness of (DASLs), and relate principal chains to "fundamental chains'' which correspond to "fundamental faces'' of simplicial complexes as introduced by Hibi.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
