Syzygies, multigraded regularity and toric varieties

Abstract

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.

improved exposition and corrected typos

References in corpus (2)

• Multiplication maps of linear systems on smooth projective toric surfaces
• Resolutions of Segre embeddings of projective spaces of any dimension

Cited by in corpus (19)

• Asymptotic syzygies of algebraic varieties
• Koszul homology and syzygies of Veronese subalgebras
• Quiver representations in toric geometry
• Linear determinantal equations for all projective schemes
• Representation stability for syzygies of line bundles on Segre--Veronese varieties
• On the Ext-computability of Serre quotient categories
• Syzygies of Curves in Products of Projective Spaces
• Generation and syzygies of the first secant variety
• Vanishing theorems and the multigraded regularity of nonsingular subvarieties
• Cox rings and symplectic quotient singularities with torus action
• Adjoint line bundles and syzygies of projective varieties
• Multigraded regularity and the Koszul property
• Linear syzygies of curves in weighted projective space
• Mori Dream Spaces as fine moduli of quiver representations
• Regularity of smooth curves in biprojective spaces
• Semigroup Graded Stillman's Conjecture
• Arithmetic properties of the first secant variety to a projective variety
• Regularity and Segre-Veronese embeddings
• Syzygies of some GIT quotients