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