✦ LIBER ✦

Toric sets and orbits on toric varieties

✍ Scribed by Anargyros Katsabekis; Apostolos Thoma

Publisher: Elsevier Science
Year: 2003
Tongue: English
Weight: 116 KB
Volume: 181
Category: Article
ISSN: 0022-4049
DOI: 10.1016/s0022-4049(02)00305-5

No coin nor oath required. For personal study only.

✦ Synopsis

Let D be an integer matrix. A toric set, namely the points in K n parametrized by the columns of D, and a toric variety are associated to D. The toric set is a subset of the toric variety. We describe the relation between the toric set and the toric variety, in terms of the orbits of the torus action on the toric variety. The toric set depends on the sign (+; -; 0) pattern of the matrix D. Finally, we prove that any toric variety over an algebraically closed ÿeld can be expressed as a toric set, for an appropriate matrix.

📜 SIMILAR VOLUMES

Differential operators on toric varietie

Differential operators on toric varieties

✍ Ian M. Musson 📂 Article 📅 1994 🏛 Elsevier Science 🌐 English ⚖ 731 KB

Families of toric varieties

✍ Mihai Halic 📂 Article 📅 2003 🏛 John Wiley and Sons 🌐 English ⚖ 351 KB

## Abstract The goal of this article is to construct families of complete toric varieties over arbitrary bases, and to compute the cohomology of the total space. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

D-Modules on Smooth Toric Varieties

✍ Mircea Mustaţă; Gregory G Smith; Harrison Tsai; Uli Walther 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 222 KB

Let X be a smooth toric variety. Cox introduced the homogeneous coordinate ring S of X and its irrelevant ideal . Let A denote the ring of differential operators on Spec(S). We show that the category of -modules on X is equivalent to a subcategory of graded A-modules modulo -torsion. Additionally, w

On Simplicial Toric Varieties Which Are

On Simplicial Toric Varieties Which Are Set-Theoretic Complete Intersections

✍ Margherita Barile; Marcel Morales; Apostolos Thoma 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 100 KB

In this paper we prove: 1. In characteristic p ) 0 every simplicial toric affine or projective variety with full parametrization is a set-theoretic complete intersection. This extends Ž . previous results by R.

Graded rings and equivariant sheaves on

Graded rings and equivariant sheaves on toric varieties

✍ Markus Perling 📂 Article 📅 2004 🏛 John Wiley and Sons 🌐 English ⚖ 258 KB

## Abstract In this note we derive a formalism for describing equivariant sheaves over toric varieties. This formalism is a generalization of a correspondence due to Klyachko, which states that equivariant vector bundles on toric varieties are equivalent to certain sets of filtrations of vector spa

Nash problem for stable toric varieties

✍ Peter Petrov 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 154 KB

## Abstract The main result of this paper is the proof of the Nash conjecture for stable toric varieties. We also introduce the Nash problem for pairs and prove it in the case of pairs (__X__, __Y__) of a toric variety __X__ and a proper closed __T__ ‐invariant subset __Y__ containing Sing(__X__) (