Rationality questions 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 the infimum, over all curves C passing through x, of the ratios (L.C)/m, where (L.C) denotes the intersection product of L and C and m is the multiplicity of C at x. These constants were defined by J.-P. Demailly in 1990 and they shed light on the local behaviour of L at x and even say something about the nature of L and X. An important question about Seshadri constants is whether they can be irrational. They are expected to be irrational often, even though currently no examples are known. In this talk, we will focus on rational surfaces. We will discuss certain conjectures on linear systems of plane curves and show that Seshadri constants of some ample line bundles are irrational if these conjectures are true. This talk is based on joint works with B. Harbourne, \L. Farnik, J. Huizenga, D. Schmitz and T. Szemberg.

algebraic geometry

Audience: researchers in the topic

ZAG (Zoom Algebraic Geometry) seminar

Series comments: Description: ZAG seminar

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