Related papers: A specialization property of index

We prove a relative form of Verdier's specialization formula, and apply it to derive a Chern class identity predicted by string dualities.

We discuss different generalizations of the classical notion of the index of a singular point of a vector field to the case of vector fields or 1-forms on singular varieties, describe relations between them and formulae for their…

This is a survey of results on the Hilbert property of algebraic varieties, and variants of it.

In this paper, we study some properties of associated sequences of special polynomials. From the properties of associated sequences of polynomials, we derive some interesting identities of special polynomials.

Indices of vector fields on (complex analytic) singular varieties have been considered by various authors from several different viewpoints. All these indices coincide with the classical local index of Poincar\'e-Hopf when the ambient…

Let k be an algebraically closed field of odd characteristic. We describe derivations of a large class of quantizations of affine normal Poisson varieties over k.

A notion of the radial index of an isolated singular point of a 1-form on a singular (real or complex) variety is discussed. For the differential of a function it is related to the Euler characteristic of the Milnor fibre of the function. A…

In this work we study characteristic classes of possibly singular varieties embedded as a closed subvariety of a nonsingular variety. In special, we express the Schwartz-MacPherson class in terms of the $\mu$-class and Chern class of the…

Let $X$ be a proper variety over a henselian discretely valued field. An important obstruction to the existence of a rational point on $X$ is the index, the minimal positive degree of a zero cycle on $X$. This paper introduces a new…

We prove Koll\'ar's injectivity theorem for globally $F$-regular varieties.

Let R be a polynomial ring over k(u), where k is a field k and u is a finite family or inderterminates. The paper introduces the specialization of an arbitrary finitely generated R-module by the substitution of u to elements of k. This…

We define an index of a collection of 1-forms on a complex isolated complete intersection singularity corresponding to a Chern number and, in the case when the 1-forms are complex analytic, express it as the dimension of a certain algebra.

We present a semicontinuity result, proven in recent joint work with Morrow and Scholze, relating the mod $p$ singular cohomology of a smooth projective complex algebraic variety X to the de Rham cohomology of a smooth characteristic $p$…

Hilbert specialization is an important tool in Field Arithmetic and Arithmetic Geometry, which has usually been intended for polynomials, hence hypersurfaces, and at scalar values. In this article, first, we extend this tool to prime…

In this paper, we study properties of nodal orders defined over arbitrary base fields. In particular we give a classification of complete real nodal orders.

If A is an Abelian variety, endowed with a polarization L, we study the function N_A(t) which counts the number of Abelian subvarieties S in A such that for the induced polarization L|_S the Euler characteristic \chi(L|_S) is bounded above…

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,…

The aim of this article is to establish the specialization method on characteristic ideals for finitely generated torsion modules over a complete local normal domain R that is module-finite over $O[[x_1, ..., x_d]]$, where $O$ is the ring…

We consider a generalisation of the specialisation functor on Soergel bimodules and show that this generalised version still takes Soergel bimodules to Soergel modules.

In this paper, we gave some properties of binomial coefficient.