Related papers: Hypergeometric Discriminants

Hyperelliptic mapping class groups are defined either as the centralizers of hyperelliptic involutions inside mapping class groups of oriented surfaces of finite type or as the inverse images of these centralizers by the natural…

This paper investigates the stratification of the discriminant hypersurface associated with a univariate polynomial via the number of its distinct complex roots. We introduce two novel approaches different from the one based on…

There are many instances such that deformation space of the homology class of an algebraic cycle as a Hodge cycle is larger than its deformation space as algebraic cycle. This phenomena can occur for algebraic cycles inside hypersurfaces,…

The hypotenuses of all right triangles inscribed into a fixed conic $C$ with fixed right-angle vertex $p$ are incident with the Fr\'egier point $f$ to $p$ and $C$. As $p$ varies on the conic, the locus of the Fr\'egier point is, in general,…

The Euler characteristic of a finite category is defined and shown to be compatible with Euler characteristics of other types of object, including orbifolds. A formula for the cardinality of the colimit of a diagram of sets is proved,…

We study the use of the Euler characteristic for multiparameter topological data analysis. Euler characteristic is a classical, well-understood topological invariant that has appeared in numerous applications, including in the context of…

Let G be a countable discrete group and let M be a smooth proper cocompact G-manifold without boundary. The Euler operator defines via Kasparov theory an element, called the equivariant Euler class, in the equivariant K-homology of M. The…

The Euler characteristic is the only additive topological invariant for spaces of certain sort, in particular, for manifolds with some finiteness properties. A generalization of the notion of a manifold is the notion of a V-manifold. Here…

Let G be a finite, complex reflection group and f its discriminant polynomial. The fibers of f admit commuting actions of G and a cyclic group. The virtual $G\times C_m$ character given by the Euler characteristic of the fiber is a…

The Euler-Koszul complex is the fundamental tool in the homological study of A-hypergeometric differential systems and functions. We compare Euler-Koszul homology with D-module direct images from the torus to the base space through orbits…

For a smooth hypersurface of even dimension, the quadratic character of the absolute Galois group defined by the determinant of the l-adic cohomology of middle dimension is computed via the square root of the discriminant of a defining…

For a partition $lambda=\{lambda_1 \geq \lambda_2 \geq \lambda_3 \}$ of non-negative integers, we calculate the Euler characteristic of the local system $V_{\lambda}$ on the moduli space of genus 3 hyperelliptic curves using a suitable…

Beauville and Donagi proved that the variety of lines $F(Y)$ of a smooth cubic fourfold $Y$ is a hyperk\"ahler variety. Recently, C. Lehn, M.Lehn, Sorger and van Straten proved that one can naturally associate a hyperK\"ahler variety $Z(Y)$…

We formalize, at the level of D-modules, the notion that A-hypergeometric systems are equivariant versions of the classical hypergeometric equations. For this purpose, we construct a functor on a suitable category of torus equivariant…

All varieties, extremal contractions, singularities are divided on exceptional and non-exceptional ones. Roughly speaking, there are the infinite families of non-exceptional varieties, extremal contractions or singularities and only the…

Double ramification loci parametrise marked curves where a weighted sum of the markings is linearly trivial; higher-rank loci are obtained by imposing several such conditions simultaneously. We obtain closed formulae for the orbifold Euler…

Datasets are mathematical objects (e.g., point clouds, matrices, graphs, images, fields/functions) that have shape. This shape encodes important knowledge about the system under study. Topology is an area of mathematics that provides…

We generalise the Vandermonde determinant identity to one which tests whether a family of hypersurfaces in $\mathbf{P}^n$ has an unexpected intersection point.

Suppose that $f$ defines a singular, complex affine hypersurface. If the critical locus of $f$ is one-dimensional, we obtain new general bounds on the ranks of the homology groups of the Milnor fiber of $f$. This result has an interesting…

We give divisibility results for the (global) characteristic varieties of hypersurface complements expressed in terms of the local characteristic varieties at points along one of the irreducible components of the hypersurface. As an…