The geometry of Weyl orbits on blow-ups of projective spaces

Abstract: Linear systems of divisors on blow-ups of projective spaces in points in general positions are connected to certain polynomial interpolation problems. While for the case of plane curves and of surfaces in 3-space there are conjectures, although long standing, formulated by M. Nagata, B. Segre and others, in the higher dimensional case we are in the dark. However, when the number of points is not too large and the blow-ups are Mori dream spaces, an action of the Weyl group on cycles of any codimension governs the birational behaviour of the space on the one hand, and the stable base locus of divisors on the other hand, and it yields a solution to the interpolation problem. Joint work with C. Brambilla, O. Dumitrescu and L. Santana Sánchez.

algebraic geometrycombinatorics

Audience: researchers in the topic

Online Nottingham algebraic geometry seminar

Series comments: Online geometry seminar, typically held on Thursday. This seminar takes place online via Microsoft Teams on the Nottingham University "Algebraic Geometry" team.

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