## Duke Mathematical Journal

### The $y$-genus of the moduli space of $\operatorname{PGL}_{n}$-Higgs bundles on a curve (for degree coprime to $n$)

#### Abstract

Building on our previous joint work with A. Schmitt, we explain a recursive algorithm to determine the cohomology of moduli spaces of Higgs bundles on any given curve (in the coprime situation). As an application of the method, we compute the $y$-genus of the space of $\operatorname{PGL}_{n}$-Higgs bundles for any rank $n$, confirming a conjecture of T. Hausel.

#### Article information

Source
Duke Math. J., Volume 162, Number 14 (2013), 2731-2749.

Dates
Revised: 1 March 2013
First available in Project Euclid: 6 November 2013

https://projecteuclid.org/euclid.dmj/1383760703

Digital Object Identifier
doi:10.1215/00127094-2381369

Mathematical Reviews number (MathSciNet)
MR3127812

Zentralblatt MATH identifier
1300.14013

#### Citation

García-Prada, Oscar; Heinloth, Jochen. The $y$ -genus of the moduli space of $\operatorname{PGL}_{n}$ -Higgs bundles on a curve (for degree coprime to $n$ ). Duke Math. J. 162 (2013), no. 14, 2731--2749. doi:10.1215/00127094-2381369. https://projecteuclid.org/euclid.dmj/1383760703

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