𝔖 Bobbio Scriptorium
✦   LIBER   ✦

D-Modules on Smooth Toric Varieties

✍ Scribed by Mircea Mustaţă; Gregory G Smith; Harrison Tsai; Uli Walther

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
222 KB
Volume
240
Category
Article
ISSN
0021-8693

No coin nor oath required. For personal study only.

✦ Synopsis

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, we prove that the characteristic variety of a -module is a geometric quotient of an open subset of the characteristic variety of the associated A-module and that holonomic -modules correspond to holonomic A-modules.

📜 SIMILAR VOLUMES

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

Cohomology on Toric Varieties and Local
Cohomology on Toric Varieties and Local Cohomology with Monomial Supports
✍ David Eisenbud; Mircea Mustaţa; Mike Stillman 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 295 KB

In this note we describe aspects of the cohomology of coherent sheaves on a complete toric variety X over a field k and, more generally, the local cohomology, with supports in a monomial ideal, of a finitely generated module over a polynomial ring S. This leads to an efficient way of computing such

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.

Involutive Varieties with Smooth Support
Involutive Varieties with Smooth Support
✍ S.C. Coutinho; D. Levcovitz 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 240 KB

We prove a structure theorem for conic involutive varieties of the cotangent bundle of a smooth algebraic variety X whose projection on X is smooth. The paper includes an example of a conic involutive variety of T ଙ X which is not the characteristic variety of any D D -module.

Limits of Compactified Jacobians and D-M
Limits of Compactified Jacobians and D-Modules on Smooth Projective Curves
✍ Rob C. Cannings; Martin P. Holland 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 276 KB

Let S be a smooth projective curve and D S its sheaf of differential operators. This paper classifies the rank one torsion-free D S -modules up to isomorphism. Such a module E has a degree which depends on the homological properties of E. Furthermore, the set of isomorphism classes with fixed degree