Diagonal splittings of toric varieties and unimodularity

  title={Diagonal splittings of toric varieties and unimodularity},
  author={Jed Chou and Milena Hering and Sam Payne and Rebecca Tramel and Ben Whitney},
We use a polyhedral criterion for the existence of diagonal splittings to investigate which toric varieties X are diagonally split. Our results are stated in terms of the vector configuration given by primitive generators of the 1-dimensional cones in the fan defining X. We show, in particular, that X is diagonally split at all q if and only if this configuration is unimodular, and X is not diagonally split at any q if this configuration is not 2-regular. We also study implications for the… 
2 Citations

Diagonal F-splitting and Symbolic Powers of Ideals

. Let J be any ideal in a strongly F -regular, diagonally F -split ring R essentially of finite type over an F -finite field. We show that J s ` t Ď τ p J s ´ ε q τ p J t ´ ε q for all s,t,ε ą 0 for

A new subadditivity formula for test ideals



Frobenius splittings of toric varieties

We discuss a characteristic free version of Frobenius splittings for toric varieties and give a polyhedral criterion for a toric variety to be diagonally split. We apply this criterion to show that

Normal polytopes, triangulations, and Koszul algebras.

This paper is devoted to the algebraic and combinatorial properties of polytopal semigroup rings defined äs follows. Let P be a lattice polytope in IR, i.e. a polytope whose vertices have integral

Globally F-regular varieties: applications to vanishing theorems for quotients of Fano varieties.

H (X, (L ⊗ ω−1) ⊗ ω) vanishes whenL ⊗ ω−1 is ample, and hence vanishing holds in particular whenever L is numerically effective andω−1 is ample. In this paper, a class of algebraic varieties is

Frobenius splitting methods in geometry and representation theory

* Preface * Frobenius Splitting: General Theory * Frobenius Splitting * Schubert Varieties * Splitting and Filtration * Cotangent Bundles of Flag Varieties * Group Embeddings * Hilbert Schemes of

Quadratic Gröbner bases for smooth 3×3 transportation polytopes

AbstractThe toric ideals of 3×3 transportation polytopes $\mathsf{T}_{\mathbf{rc}}$ are quadratically generated. The only exception is the Birkhoff polytope B3.If $\mathsf{T}_{\mathbf{rc}}$ is

Theory of linear and integer programming

  • A. Schrijver
  • Mathematics
    Wiley-Interscience series in discrete mathematics and optimization
  • 1999
Introduction and Preliminaries. Problems, Algorithms, and Complexity. LINEAR ALGEBRA. Linear Algebra and Complexity. LATTICES AND LINEAR DIOPHANTINE EQUATIONS. Theory of Lattices and Linear