# Diagonal splittings of toric varieties and unimodularity

@inproceedings{Chou2016DiagonalSO, title={Diagonal splittings of toric varieties and unimodularity}, author={Jed Chou and Milena Hering and Sam Payne and Rebecca Tramel and Ben Whitney}, year={2016} }

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

- Mathematics
- 2022

. 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…

## References

SHOWING 1-8 OF 8 REFERENCES

### Frobenius splittings of toric varieties

- Mathematics
- 2008

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.

- Mathematics
- 1997

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.

- Mathematics
- 2000

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

- Mathematics
- 2004

* 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

- Mathematics
- 2009

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

- MathematicsWiley-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…