Local positivity of line bundles on smooth toric varieties and Cayley polytopes
2016 (English)In: Journal of symbolic computation, ISSN 0747-7171, E-ISSN 1095-855X, Vol. 74, 109-124 p.Article in journal (Refereed) Published
For any non-negative 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 maximal k-th osculating dimension, but not maximal (k + 1)-th osculating dimension, at every point 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.
Place, publisher, year, edition, pages
2016. Vol. 74, 109-124 p.
osculating space, Seshadri consant, k-jet ampleness, toric variety, Cayley polytope, lattice polytope
IdentifiersURN: urn:nbn:se:kth:diva-134705DOI: 10.1016/j.jsc.2015.05.007ISI: 000366794100006ScopusID: 2-s2.0-84948718076OAI: oai:DiVA.org:kth-134705DiVA: diva2:667763
FunderSwedish Research Council, NT:2010-5563
QC 201601212013-11-272013-11-272016-02-02Bibliographically approved