Tropical degenerations and irrationality of hypersurfaces in products of projective spaces

Abstract: The specialization map for stable birational types associates with every strictly toroidal one-parameter degeneration an obstruction to the stable rationality of a very general fiber. In many applications, suitable degenerations can be constructed by hand, but there are also cases where the complexity gets too high to write down explicit equations, and one needs to rely on tropical geometry to give a combinatorial description in terms of regular subdivisions of Newton polytopes. I will illustrate this technique for hypersurfaces in products of projective spaces. This is based on joint work with John Christian Ottem.

algebraic geometrycombinatorics

Audience: researchers in the topic

(LAGARTOS) Latin American Real and Tropical Geometry Seminar

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