1. Hodge polynomials of the SL(2, C)-character variety of an elliptic curve with two marked points
- Author
-
Marina Logares and Vicente Muñoz
- Subjects
Instanton ,Pure mathematics ,Betti number ,Matemáticas ,General Mathematics ,Hodge theory ,Diagonal ,Mathematical analysis ,Character variety ,Moduli space ,Elliptic curve ,Mathematics - Algebraic Geometry ,Conjugacy class ,Mathematics::Algebraic Geometry ,FOS: Mathematics ,14D20, 14C30, 14L24 ,Algebraic Geometry (math.AG) ,Mathematics::Symplectic Geometry ,Mathematics - Abstract
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., 21 pages; v2. Accepted for publication in Internat. J. Math. v3. Mistake in polynomial of Theorem 1.1(3) corrected
- Published
- 2014