Syzygies of Projective Toric Varieties
نویسنده
چکیده
We study the equations defining a projective embedding of a toric variety X using multigraded Castelnuovo-Mumford regularity. Consider globally generated line bundles B1, . . . , Bl and an ample line bundle L := B ⊗m1 1 ⊗ B2 2 ⊗ · · · ⊗ Bl l on X . This article gives sufficient conditions on mi ∈ N to guarantee that the homogeneous ideal I of X in P := P (
منابع مشابه
Syzygies, multigraded regularity and toric varieties
Using multigraded Castelnuovo-Mumford regularity, we study the equations defining a projective embedding of a variety X . Given globally generated line bundles B1, . . . , Bl on X and m1, . . . , ml ∈ N, consider the line bundle L := B m1 1 ⊗ · · · ⊗ Bl l . We give conditions on the mi which guarantee that the ideal of X in P(H (X, L)∗) is generated by quadrics and the first p syzygies are line...
متن کاملSyzygies, Regularity and Toric Varieties
Let A be an ample line bundle on a projective toric variety X of dimension n. We show that if l ≥ n− 1 + p, then A satisfies the property Np. Applying similar methods, we obtain a combinatorial theorem: For a given lattice polytope P we give a criterion for an integer m to guarantee that mP is normal.
متن کاملRepresentation Stability for Syzygies of Line Bundles on Segre–veronese Varieties
The rational homology groups of the packing complexes are important in algebraic geometry since they control the syzygies of line bundles on projective embeddings of products of projective spaces (Segre–Veronese varieties). These complexes are a common generalization of the multidimensional chessboard complexes and of the matching complexes of complete uniform hypergraphs, whose study has been ...
متن کاملm at h . A G ] 2 6 M ay 1 99 8 Quasi - Projective Reduction of Toric Varieties
We define a quasi–projective reduction of a complex algebraic variety X to be a regular map from X to a quasi–projective variety that is universal with respect to regular maps from X to quasi–projective varieties. A toric quasi–projective reduction is the analogous notion in the category of toric varieties. For a given toric variety X we first construct a toric quasi–projective reduction. Then ...
متن کاملGeometric invariant theory and projective toric varieties
We define projective GIT quotients, and introduce toric varieties from this perspective. We illustrate the definitions by exploring the relationship between toric varieties and polyhedra. Geometric invariant theory (GIT) is a theory of quotients in the category of algebraic varieties. Let X be a projective variety with ample line bundle L, and G an algebraic group acting on X, along with a lift...
متن کامل