#Princeton algebraic geometry seminar how to

#Princeton algebraic geometry seminar how to

After discussing the definition of local positivity and how to measure it, we explain a way to describe local positivity in terms of Newton-Okounkov bodies. (Küronya): The main theme of the talk is positivity of line bundles at a given point on a projective variety.

As an application we define a degree of rationality in a natural way and we provide a classification result for small values. Inspired by their result we prove a stronger version of the criterion, namely we give necessary and sufficient conditions for the local ring of X at a point x to be C-isomorphic to the local ring of a point of the projective space. In 2006 Ionescu and Russo gave a criterion that describes rationality in terms of suitable families of rational curves through a point of X. Properties of special families of rational curves capture the geometry of X. (Fusi): Let X be a complex projective variety. Our motivating example will be plane elliptic cubics defined over a non-Archimedean valued field. In this talk, I will show how to use linear tropical modifications and Berkovich skeleta to achieve such goal in the curve case. Thus, the task of funding a suitable embedding or of repairing a given 'bad' embedding to obtain a nicer tropicalization that better reflects the geometry of the input object becomes essential for many applications.

One general difficulty in this approach is that tropicalization strongly depends on the embedding of the algebraic variety. Often, we can derive classical statements from these (easier) combinatorial objects. (Cueto): Tropical geometry is a piecewise-linear shadow of algebraic geometry that preserves important geometric invariants. Zassenhaus Lectures: Curve Counting in Various Dimensionsĭeformation of Quintic Threefolds to the Chordal VarietyĮffective Chabauty for symmetric powers of curves Motivic zeta functions and infinite cyclic covers Hall algebras: algebraic and geometric variationsĬomputing linear systems on metric graphs On the problem of deformation of rational and nearly rational varieties The Business of Hodge Theory and Algebraic Cycles The Bernstein-Sato polynomial and the Strong Monodromy Conjectureīernstein-Sato polynomials for maximal minors and sub-maximal PfaffiansĮquivariant K-theory of smooth projective spherical varieties Wall-crossing for genus zero K-theoretic quasimap theory Limits of plane curves via stacky branched coversĮynard-Orantin topological recursion and equivariant Gromov-Witten invariants of the projective lineĮnumerative Dualities for a family of Calabi-Yau Threefolds Toric vector bundles and parliaments of polytopes Skeletons, degenerations, and Gromov-Witten theoryĮxcluded homeomorphism types for dual complexes of surfaces Relative orbifold Donaldson-Thomas theory and local gerby curvesīrick varieties and the toric variety of the associahedron Non-abelian and Spherical Tropicalization Toric degenerations and symplectic geometry of projective varieties Local positivity in terms of Newton-Okounkov bodies Repairing tropical curves by means of linear tropical modifications Ohio State University Algebraic Geometry Seminar