Frobenius splittings of toric varieties

@article{Payne2008FrobeniusSO,
  title={Frobenius splittings of toric varieties},
  author={Sam Payne},
  journal={arXiv: Algebraic Geometry},
  year={2008}
}
  • S. Payne
  • Published 28 February 2008
  • Mathematics
  • arXiv: Algebraic Geometry
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 section rings of nef line bundles on diagonally split toric varieties are normally presented and Koszul, and that Schubert varieties are not diagonally split in general. 

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References

SHOWING 1-10 OF 59 REFERENCES

Koszul Property and Frobenius Splitting of Schubert Varieties

We show how the Frobenius splitting method of Mehta-Ramanathan implies the Koszul property of projective coordinate rings of Schubert varieties.

On the classification of toric fano varieties

  • G. Ewald
  • Mathematics
    Discret. Comput. Geom.
  • 1988
Toric Fano varieties are algebraic varieties associated with a special class of convex polytopes in R′' using a purely combinatorial method of proof.

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

Classification of toric Fano 5-folds

We obtain 866 isomorphism classes of five-dimensional nonsingular toric Fano varieties using a computer program and the database of four-dimensional reflexive polytopes. The algorithm is based on the

Splitting of the direct image of sheaves under the Frobenius

A generalisation and a new proof are given of a recent result of J. F. Thomsen (1996), which says that for L a line bundle on a smooth toric variety X over a field of positive characteristic, the

Multiplication maps and vanishing theorems for Toric varieties

We use multiplication maps to give a characteristic-free approach to vanishing theorems on toric varieties. Our approach is very elementary but is enough powerful to prove vanishing theorems.

Gröbner bases and convex polytopes

Grobner basics The state polytope Variation of term orders Toric ideals Enumeration, sampling and integer programming Primitive partition identities Universal Grobner bases Regular triangulations The

On the homogeneous ideal of a projective nonsingular toric variety

Reason for withdrawal: There is a serious mistake in the calculation of the divisor of the rational section used in the proof of Prop. 2.2.1., and with the correct value the argument does not work.

Cayley decompositions of lattice polytopes and upper bounds for h*-polynomials

Abstract We give an effective upper bound on the h*-polynomial of a lattice polytope in terms of its degree and leading coefficient, confirming a conjecture of Batyrev. We deduce this bound as a
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