Abstract
A set of points Z in ℙ³ is an (a,b)-geproci set (for GEneral PROjection is a Complete Intersection) if its projection from a general point to a plane is a complete intersection of curves of degrees a and b. we will report on some results in order to pursue classification of geproci sets. Specifically, we will show how to classify (m,n)-geproci sets Z which consist of m points on each...
Abstract
Magnitude was first introduced by Leinster in 2008 [1]. It is a notion analogous to the Euler characteristic of a category, and it captures the structure and complexity of a metric space. Magnitude homology was defined in 2014 by Hepworth and Willerton [2] as a categorification of magnitude in the context of simple undirected graphs, and although the construction of the boundary map...
Abstract
The Nakai-Moishezon criterion in algebraic geometry and Yau's solution of the Calabi conjecture, when taken together, can be viewed as establishing a correspondence between the solvability of the complex Monge-Ampère equation and the positivity of certain intersection numbers involving proper subvarieties. In complex geometry, many other examples of such correspondences have been...
Abstract
We investigate the problems of unirationality and rationality for conic bundles S→P1 over a C1 field k, which can be described as the zero locus of a hypersurface in the projectivization of a rank-3 vector bundle over P1. Conic bundles can be classified by the degree d of the discriminant, i.e. the number of points on the base where the corresponding fiber is not a smooth conic....
Abstract
We establish a correspondence between one-parameter deformations of an affine Gorenstein toric variety X, defined by a polytope P, and mutations of a Laurent polynomial f, whose Newton polytope is equal to P. If the Newton polytope P of f is two dimensional and there exists a set of mutations of f that mutate P to a smooth polygon, then, under certain assumptions, we show that the...
