Multigraded CastelnuovoMumford Regularity
Abstract
We develop a multigraded variant of CastelnuovoMumford regularity. Motivated by toric geometry, we work with modules over a polynomial ring graded by a finitely generated abelian group. As in the standard graded case, our definition of multigraded regularity involves the vanishing of graded components of local cohomology. We establish the key properties of regularity: its connection with the minimal generators of a module and its behavior in exact sequences. For an ideal sheaf on a simplicial toric variety X, we prove that its multigraded regularity bounds the equations that cut out the associated subvariety. We also provide a criterion for testing if an ample line bundle on X gives a projectively normal embedding.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 May 2003
 arXiv:
 arXiv:math/0305214
 Bibcode:
 2003math......5214M
 Keywords:

 Mathematics  Commutative Algebra;
 Mathematics  Algebraic Geometry;
 14M25;
 13D45;
 14Q20
 EPrint:
 30 pages, 5 figures