summer 2018 



Jarosław Buczyński, Uniwersytet Warszawski 05.06.2024 14:00, B137 Title: Fujita vanishing, sufficiently ample line bundles, and cactus varieties
For a fixed projective variety X, we say that a property P(L) (where L is a line bundle on X) is satisfied by sufficiently ample line bundles if there exists a line bundle M on X such that P(L) hold for any L with LM ample. I will discuss which properties of line bundles are satisfied by the sufficiently ample line bundles  for example, can you figure out before the talk, whether a sufficiently ample line bundle must be very ample? The grandfather of such properties and a basic ingredient used to study this concept is Fujita's vanishing theorem, which is an analogue of Serre's vanishing for sufficiently ample line
bundles. At the end of the talk I will define cactus varieties (an analogue of secant varieties) and sketch a proof that cactus varieties to sufficiently ample embeddings of X are (settheoretically) defined by minors of matrices with linear entries. The topic is closely related to conjectures of EisenbudKohStillman (for curves) and SidmanSmith (for any varieties). The new ingredients are based on a joint work in preparation with Weronika Buczyńska and Łucja Farnik.


Last modified: 16.11.2022 