Okounkov Bodies and Nagata type Conjectures

Okounkov Bodies and Nagata type Conjectures

22 September -  28 September, 2013 | Warsaw

Announcements

viewThe focus of the workshop is the theory of linear series on projective varieties. This is a vast and traditional research area in algebraic geometry with many facets, of which the workshop will concentrate on specific two that have recently attracted a lot of attention and witnessed new significant developments. Namely, we plan to discuss the theory of Newton-Okounkov bodies whose systematic study has been recently initiated and has witnessed a rapid development in both theory and applications ever since. In addition, to becoming fundamental to the study of positive line bundles and uniting interesting work coming from projective and complex analytic geometry, this new circle of ideas has found many application outside algebraic geometry, for instance in combinatorics and representation theory. For linear series Okounkov bodies constitute a concise and accessible way to express and control various asymptotic invariants, and measure the positivity properties of the underlying divisors. The traditional Nagata Conjecture can be expressed in asymptotic terms using either Seshadri constants or Waldschmidt constants. Recently it has become apparent that Nagata Conjecture for points in the projective plane is a manifestation of a much more general picture concerning configurations of disjoint linear subspaces of a projective space. The aim of the research group is to investigate to what extend methods in Okounkov bodies can be applied or modified in order to apply towards very concrete questions emerging from these Nagata type conjectures.

For more details see the official page of the workshop.