A Correspondence between Hilbert Polynomials and Chern Polynomials over Projective Spaces
نویسنده
چکیده
We construct a map ζ from K0(P) to (Z[x]/xd+1)× × Z, where (Z[x]/xd+1)× is a multiplicative Abelian group with identity 1, and show that ζ induces an isomorphism between K0(P) and its image. This is inspired by a correspondence between Chern and Hilbert polynomials stated in Eisenbud [1, Exercise 19.18]. The equivalence of these two polynomials over Pd is discussed in this paper.
منابع مشابه
Using Grothendieck Groups to Define and Relate the Hilbert and Chern Polynomials Axiomatically
The Hilbert polynomial can be defined axiomatically as a group homomorphism on the Grothendieck group K(X) of a projective variety X, satisfying certain properties. The Chern polynomial can be similarly defined. We therefore define these rather abstract notions to try and find a nice description of this relationship. Introduction Let X = P be a complex projective variety over an algebraically c...
متن کاملJack Polynomials and Hilbert Schemes of Points on Surfaces
The Jack (symmetric) polynomials P (α) λ (x) form a class of symmetric polynomials which are indexed by a partition λ and depend rationally on a parameter α. They reduced to the Schur polynomials when α = 1, and to other classical families of symmetric polynomials for several specific parameters. Recently they attracts attention from various points of view, for example the integrable systems an...
متن کاملThe geometry of the parabolic Hilbert schemes
Let X be a smooth projective surface and D be a smooth divisor over an algebraically closed field k. In this paper, we discuss the moduli schemes of the ideals of points of X with parabolic structures at D. They are called parabolic Hilbert schemes. The first result is that the parabolic Hilbert schemes are smooth. And then some of the studies of Ellingsrud-Strømme, Göttsche, Cheah, Nakajima an...
متن کاملThe Cohomology Rings of Hilbert Schemes via Jack Polynomials
Fundamental and deep connections have been developed in recent years between the geometry of Hilbert schemes X [n] of points on a (quasi-)projective surface X and combinatorics of symmetric functions. Among distinguished classes of symmetric functions, let us mention the monomial symmetric functions, Schur polynomials, Jack polynomials (which depend on a Jack parameter), and Macdonald polynomia...
متن کاملComposition collisions and projective polynomials
The functional decomposition of polynomials has been a topic of great interest and importance in pure and computer algebra and their applications. The structure of compositions of (suitably normalized) polynomials f = g ◦ h in Fq[x] is well understood in many cases, but quite poorly when the degrees of both components are divisible by the characteristic p. This work investigates the decompositi...
متن کامل