The Euler–Poincaré characteristic of joint reductions and mixed multiplicities

2020 ◽  
pp. 2150026
Author(s):  
Truong Thi Hong Thanh ◽  
Duong Quoc Viet
Keyword(s):  
Hilbert Polynomial

This paper defines the Euler–Poincaré characteristic of joint reductions of ideals which concerns the maximal terms in the Hilbert polynomial; characterizes the positivity of mixed multiplicities in terms of minimal joint reductions; proves the additivity and other elementary properties for mixed multiplicities. The results of the paper together with the results of [Thanh and Viet, Mixed multiplicities of maximal degrees, J. Korean Math. Soc. 55(3) (2018) 605–622] seem to show a natural and nice picture of mixed multiplicities of maximal degrees.

scholarly journals Sharp upper bounds for the Betti numbers of a given Hilbert polynomial

2013 ◽  
Vol 7 (5) ◽  
pp. 1019-1064 ◽  
Author(s):  
Giulio Caviglia ◽  
Satoshi Murai
Keyword(s):  
Betti Numbers ◽  
Upper Bounds ◽  
Hilbert Polynomial

scholarly journals A trace formula for vector-valued modular forms

2015 ◽  
Vol 17 (06) ◽  
pp. 1550069
Author(s):  
P. Bantay
Keyword(s):  
Trace Formula ◽  
Modular Forms ◽  
Weight Distribution ◽  
Hilbert Polynomial ◽  
Free Generators ◽  
Vector Valued

We present a formula for vector-valued modular forms, expressing the value of the Hilbert-polynomial of the module of holomorphic forms evaluated at specific arguments in terms of traces of representation matrices, restricting the weight distribution of the free generators.

scholarly journals On the Singular Sheaves in the Fine Simpson Moduli Spaces of 1-dimensional Sheaves

2017 ◽  
Vol 60 (3) ◽  
pp. 522-535 ◽  
Author(s):  
Oleksandr Iena ◽  
Alain Leytem
Keyword(s):  
Projective Plane ◽  
Moduli Space ◽  
Moduli Spaces ◽  
Blow Up ◽  
Line Bundles ◽  
Hilbert Polynomial ◽  
Stable Sheaves ◽  
Closed Subvariety

AbstractIn the Simpson moduli space M of semi-stable sheaves with Hilbert polynomial dm − 1 on a projective plane we study the closed subvariety M' of sheaves that are not locally free on their support. We show that for d ≥4 , it is a singular subvariety of codimension 2 in M. The blow up of M along M' is interpreted as a (partial) modification of M \ M' by line bundles (on support).

scholarly journals On the Chern numbers and the Hilbert polynomial of an almost complex manifold with a circle action

2017 ◽  
Vol 19 (04) ◽  
pp. 1750043 ◽  
Author(s):  
Silvia Sabatini
Keyword(s):  
Fixed Points ◽  
Complex Manifold ◽  
Index Formula ◽  
Circle Action ◽  
Hilbert Polynomial ◽  
Dimensional Manifold ◽  
Hamiltonian Action ◽  
Almost Complex Manifold ◽  
Almost Complex ◽  
Chern Numbers

Let [Formula: see text] be a compact, connected, almost complex manifold of dimension [Formula: see text] endowed with a [Formula: see text]-preserving circle action with isolated fixed points. In this paper, we analyze the “geography problem” for such manifolds, deriving equations relating the Chern numbers to the index [Formula: see text] of [Formula: see text]. We study the symmetries and zeros of the Hilbert polynomial, which imply many rigidity results for the Chern numbers when [Formula: see text]. We apply these results to the category of compact, connected symplectic manifolds. A long-standing question posed by McDuff and Salamon asked about the existence of non-Hamiltonian actions with isolated fixed points. This question was answered recently by Tolman, with an explicit construction of a 6-dimensional manifold with such an action. One issue that this raises is whether one can find topological criteria that ensure the manifold can only support a Hamiltonian or only a non-Hamiltonian action. In this vein, we are able to deduce such criteria from our rigidity theorems in terms of relatively few Chern numbers, depending on the index. Another consequence is that, if the action is Hamiltonian, the minimal Chern number coincides with the index and is at most [Formula: see text].

scholarly journals Moduli of Space Sheaves with Hilbert Polynomial 4m+ 1

2018 ◽  
Vol 61 (2) ◽  
pp. 328-345 ◽  
Author(s):  
Mario Maican
Keyword(s):  
Euler Characteristic ◽  
Moduli Space ◽  
Elementary Proof ◽  
Hilbert Polynomial ◽  
Space Curves ◽  
Irreducible Components

AbstractWe investigate the moduli space of sheaves supported on space curves of degree and having Euler characteristic 1. We give an elementary proof of the fact that this moduli space consists of three irreducible components.

scholarly journals On the set of Hilbert polynomials

2001 ◽  
Vol 64 (2) ◽  
pp. 291-305 ◽  
Author(s):  
Alexander B. Levin
Keyword(s):  
Chromatic Polynomial ◽  
Hilbert Polynomial ◽  
Graded Algebra ◽  
Open Problems ◽  
Graded Algebras ◽  
Hilbert Polynomials

We characterise the set of all Hilbert polynomials of standard graded algebras over a field and give solutions of some open problems on Hilbert polynomials. In particular, we prove that a chromatic polynomial of a graph is a Hilbert polynomial of some standard graded algebra.

Sign in / Sign up

Export Citation Format

Share Document