Mapping toric varieties into low dimensional spaces

Dufresne, Emilie; Jeffries, Jack

Abstract

A smooth d-dimensional projective variety X can always be embedded into 2d + 1-dimensional space. In contrast, a singular variety may require an arbitrary large ambient space. If we relax our requirement and ask only that the map is injective, then any d-dimensional projective variety can be mapped injectively to 2d + 1-dimensional projective space. A natural question then arises: what is the minimal m such that a projective variety can be mapped injectively to m-dimensional projective space? In this paper we investigate this question for normal toric varieties, with our most complete results being for Segre-Veronese varieties.

Citation

Dufresne, E., & Jeffries, J. (in press). Mapping toric varieties into low dimensional spaces. Transactions of the American Mathematical Society, 1. https://doi.org/10.1090/tran/7026

• Journal Article Type: Article
• Acceptance Date: Jul 19, 2016
• Online Publication Date: Apr 26, 2017
• Deposit Date: May 24, 2018
• Publicly Available Date: May 24, 2018
• Journal: Transactions of the American Mathematical Society
• Print ISSN: 0002-9947
• Electronic ISSN: 1088-6850
• Publisher: American Mathematical Society
• Peer Reviewed: Peer Reviewed
• Pages: 1
• DOI: https://doi.org/10.1090/tran/7026
• Keywords: Segre-Veronese varieties; Dimension of secant variety; Torus invariants; Separating invariants; Local cohomology
• Public URL: https://nottingham-repository.worktribe.com/output/800329
• Related Public URLs: http://www.ams.org/journals/tran/earlyview/#tran7026