Vol. 2, No. 2, 2008

Download this article
Download this article For screen
For printing
Recent Issues

Volume 10
Issue 9, 1845–2052
Issue 8, 1601–1843
Issue 7, 1373–1600
Issue 6, 1147–1371
Issue 5, 939–1146
Issue 4, 695–938
Issue 3, 451–694
Issue 2, 215–450
Issue 1, 1–214

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
Cover
Editorial Board
Editors' Addresses
Editors' Interests
About the Journal
Scientific Advantages
Submission Guidelines
Submission Form
Subscriptions
Editorial Login
Contacts
Author Index
To Appear
 
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Piecewise polynomials, Minkowski weights, and localization on toric varieties

Eric Katz and Sam Payne

Vol. 2 (2008), No. 2, 135–155
Abstract

We use localization to describe the restriction map from equivariant Chow cohomology to ordinary Chow cohomology for complete toric varieties in terms of piecewise polynomial functions and Minkowski weights. We compute examples showing that this map is not surjective in general, and that its kernel is not always generated in degree one. We prove a localization formula for mixed volumes of lattice polytopes and, more generally, a Bott residue formula for toric vector bundles.

Keywords
toric variety, localization, tropical geometry, piecewise polynomial, Minkowski weight
Mathematical Subject Classification 2000
Primary: 14M25
Secondary: 14C17, 52B20
Milestones
Received: 2 April 2007
Revised: 22 October 2007
Accepted: 20 November 2007
Published: 15 March 2008
Authors
Eric Katz
Department of Mathematics
University of Texas
Austin, TX 78712
United States
Sam Payne
Department of Mathematics, Bldg 380
Stanford University
Stanford, CA 94305
United States