Positivity, Adjoint Linear Systems, and Jet Separation

Abstract: Positivity of line bundles allows us to construct morphisms and projective embeddings, and more generally global sections with prescribed Taylor coefficients. This raises a quantitative question: how much positivity is needed for global generation, very ampleness, or separation of higher-order jets? In this expository talk, I will discuss these questions for adjoint line bundles $K_X+mA$ with $A$ ample, starting from Fujita’s conjectures. I will also present global and local criteria for $k$-jet separation and the role of Seshadri constants in measuring local positivity.

algebraic geometry

Audience: researchers in the discipline

ODTU-Bilkent Algebraic Geometry Seminars