scholarly journals Local comparisons of homological and homotopical mixed Hodge polynomials

2020 ◽  
Vol 96 (3) ◽  
pp. 28-31
Author(s):  
Shoji Yokura
Keyword(s):  
Hodge Polynomials

scholarly journals HODGE POLYNOMIALS OF THE MODULI SPACES OF PAIRS

2007 ◽  
Vol 18 (06) ◽  
pp. 695-721 ◽  
Author(s):  
VICENTE MUÑOZ ◽  
DANIEL ORTEGA ◽  
MARIA-JESÚS VÁZQUEZ-GALLO
Keyword(s):  
Moduli Spaces ◽  
Holomorphic Section ◽  
Complex Numbers ◽  
Projective Curve ◽  
Hodge Structures ◽  
Smooth Projective Curve ◽  
Holomorphic Bundle ◽  
Rank 2 ◽  
Hodge Polynomials ◽  
Mixed Hodge Structures

Let X be a smooth projective curve of genus g ≥ 2 over the complex numbers. A holomorphic pair on X is a couple (E, ϕ), where E is a holomorphic bundle over X of rank n and degree d, and ϕ ∈ H0(E) is a holomorphic section. In this paper, we determine the Hodge polynomials of the moduli spaces of rank 2 pairs, using the theory of mixed Hodge structures. We also deal with the case in which E has fixed determinant.

scholarly journals HODGE POLYNOMIALS OF THE MODULI SPACES OF TRIPLES OF RANK (2, 2)

2008 ◽  
Vol 60 (2) ◽  
pp. 235-272 ◽  
Author(s):  
V. Munoz ◽  
D. Ortega ◽  
M.-J. Vazquez-Gallo
Keyword(s):  
Moduli Spaces ◽  
Rank 2 ◽  
Hodge Polynomials

scholarly journals HODGE POLYNOMIALS OF SOME MODULI SPACES OF COHERENT SYSTEMS

2013 ◽  
Vol 24 (03) ◽  
pp. 1350014
Author(s):  
CRISTIAN GONZÁLEZ–MARTÍNEZ
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Coherent Systems ◽  
Determinantal Varieties ◽  
Hodge Polynomials

When k < n, we study the coherent systems that come from a BGN extension in which the quotient bundle is strictly semistable. In this case we describe a stratification of the moduli space of coherent systems. We also describe the strata as complements of determinantal varieties and we prove that these are irreducible and smooth. These descriptions allow us to compute the Hodge polynomials of this moduli space in some cases. In particular, we give explicit computations for the cases in which (n, d, k) = (3, d, 1) and d is even, obtaining from them the usual Poincaré polynomials.

scholarly journals Hodge polynomials of the SL(2, ℂ)-character variety of an elliptic curve with two marked points

2014 ◽  
Vol 25 (14) ◽  
pp. 1450125 ◽  
Author(s):  
Marina Logares ◽  
Vicente Muñoz
Keyword(s):  
Elliptic Curve ◽  
Moduli Space ◽  
Betti Numbers ◽  
Conjugacy Classes ◽  
Character Variety ◽  
Higgs Bundles ◽  
Hodge Numbers ◽  
Hodge Polynomials ◽  
Marked Points

We compute the Hodge polynomials for the moduli space of representations of an elliptic curve with two marked points into SL(2, ℂ). When we fix the conjugacy classes of the representations around the marked points to be diagonal and of modulus one, the character variety is diffeomorphic to the moduli space of strongly parabolic Higgs bundles, whose Betti numbers are known. In that case we can recover some of the Hodge numbers of the character variety. We extend this result to the moduli space of doubly periodic instantons.

scholarly journals On the Euler characteristics of certain moduli spaces of 1-dimensional subschemes

2017 ◽  
Author(s):  
◽  
Mazen M. Alhwaimel
Keyword(s):  
Generating Function ◽  
Moduli Spaces ◽  
Projective Variety ◽  
Smooth Projective Variety ◽  
Euler Characteristics ◽  
Torus Actions ◽  
3 Dimensional ◽  
Hodge Polynomials

Generalizing the ideas in [LQ] and using virtual Hodge polynomials as well as torus actions, we compute the Euler characteristics of some moduli spaces of 1-dimensional closed subschemes when the ambient smooth projective variety admits a Zariskilocally trivial fibration to a codimension-1 base. As a consequence, we partially verify a conjecture of W.-P. Li and Qin [LQ]. We also calculate the generating function for the number of certain punctual 3-dimensional partitions, which is used to compute the above Euler characteristics.

scholarly journals Hodge polynomials of singular hypersurfaces

2011 ◽  
Vol 60 (3) ◽  
pp. 661-673 ◽  
Author(s):  
Anatoly Libgober ◽  
Laurentiu Maxim
Keyword(s):  
Hodge Polynomials

scholarly journals Geometric determination of the Poles of Highest and second Highest order of Hodge And motivic Zeta functions

2004 ◽  
Vol 176 ◽  
pp. 1-18
Author(s):  
B. Rodrigues
Keyword(s):  
Zeta Function ◽  
Arbitrary Dimension ◽  
Zeta Functions ◽  
Motivic Zeta Functions ◽  
Hodge Polynomials ◽  
Motivic Zeta Function

AbstractTo any f ∈ ℂ[x1, … ,xn] \ ℂ with f(0) = 0 one can associate the motivic zeta function. Another interesting singularity invariant of f-1{0} is the zeta function on the level of Hodge polynomials, which is actually just a specialization of the motivic one. In this paper we generalize for the Hodge zeta function the result of Veys which provided for n = 2 a complete geometric determination of the poles. More precisely we give in arbitrary dimension a complete geometric determination of the poles of order n − 1 and n. We also show how to obtain the same results for the motivic zeta function.

Sign in / Sign up

Export Citation Format

Share Document