Syzygies, multigraded regularity and toric varieties

Details Syzygies, multigraded regularity and toric varieties Syzygies, multigraded regularity and toric varieties

2005-02-11

arxiv.org/abs/math/0502240v2

Compositio Mathematica 142 (2006) 1499-1506

Mathematics

Algebraic Geometry

improved exposition and corrected typos

Scientific paper

10.1112/S0010437X0600251X

Using multigraded Castelnuovo-Mumford regularity, we study the equations defining a projective embedding of a variety X. Given globally generated line bundles B_1, ..., B_k on X and integers m_1, ..., m_k, consider the line bundle L := B_1^m_1 \otimes ... \otimes B_k^m_k. We give conditions on the m_i which guarantee that the ideal of X in P(H^0(X,L)) is generated by quadrics and the first p syzygies are linear. This yields new results on the syzygies of toric varieties and the normality of polytopes.

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