Seminario de Geometría y Topología

Expositor: Lara Bossinger

Procedencia: IMUNAM Oaxaca

Resumen: Toric degenerations of projective varieties can be constructed in several ways. One method uses valuations on the homogeneous coordinate ring of the (polarized) projective variety and the associated Newton-Okounkov body (NO-body). If the image of the valuation (the value semigroup) is finitely generated, the NO-body is a rational polytope. In this case it defines a projective toric variety that is a flat degeneration of the projective variety we started with. It is hence desirable to test for a given valuation if its value semigroup is finitely generated. I will present a criterion for this property using higher Groebner theory and explain two applications of the theorem for Grassmannians.