Local positivity of line bundles on smooth toric varieties and Cayley polytopes. (May 2016)

• Record Type: Journal Article
• Authors: Lundman, Anders
• Is Part Of: Journal of symbolic computation. Volume 74(2016)
• Page Start: 109
• Page End: 124
• Publication Date: 2016-05
• Subjects: Osculating space -- Seshadri constant -- k-jet ampleness -- Toric variety -- Cayley polytope -- Lattice polytope; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2015.05.007
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: For any positive integer k the k -th osculating dimension at a given point x of a variety X embedded in projective space gives a measure of the local positivity of order k at that point. In this paper we show that a smooth toric embedding having the property that at every point the t -th osculating dimension is maximal if and only if t ≤ k, is associated to a Cayley polytope of order k . This result generalises an earlier characterisation by David Perkinson. In addition we prove that the above assumptions are equivalent to requiring that the Seshadri constant is exactly k at every point of X, generalising a result of Atsushi Ito.