Some recent results on Seshadri constants

Abstract: Let X be a projective variety, and let L be an ample line bundle on X. For a point x in X, the Seshadri constant of L at x is defined as the infimum, taken over all curves C passing through x, of the ratios  \frac {L.C}{m} where L.C denotes the intersection product of L and C, and m is the multiplicity of C at x. This concept was introduced by J.-P. Demailly in 1990, inspired by Seshadri’s ampleness criterion. Seshadri constants provide insights into both the local behavior of L at x and certain global properties of X. The notion of Seshadri constants has  been extended to vector bundles of arbitrary rank by C. Hacon.  We will give an overview of the current research in this area and discuss some recent results.

Host: Roya Beheshti