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

DOI10.1215/00127094-2381369zbMath1300.14013arXiv1207.5614OpenAlexW2953066573MaRDI QIDQ2016421

Jochen Heinloth, Oscar García-Prada

Publication date: 20 June 2014

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1207.5614

zbMATH Keywords

E-polynomialwall crossingmoduli space of Higgs bundlesHodge polynomial\(\mathrm{PGL}_{n}\)-Higgs bundlesy-genus

Mathematics Subject Classification ID

Complex-analytic moduli problems (32G13) Algebraic moduli problems, moduli of vector bundles (14D20) Vector bundles on curves and their moduli (14H60) Transcendental methods, Hodge theory (algebro-geometric aspects) (14C30)

Related Items

An elementary discussion of the representation and geometric invariant theory of equioriented quivers of type D with an application to quiver bundles, The intersection form on moduli spaces of twisted \(\mathrm{PGL}_n\)-Higgs bundles vanishes, Classification of the automorphism and isometry groups of Higgs bundle moduli spaces, On the Voevodsky motive of the moduli space of Higgs bundles on a curve, Arakelov–Milnor inequalities and maximal variations of Hodge structure, Intersection cohomology of character varieties for punctured Riemann surfaces, Motives of moduli spaces of bundles on curves via variation of stability and flips, Twisted spectral correspondence and torus knots, Serre polynomials of \(\mathrm{SL}_n\)- and \(\mathrm{PGL}_n\)-character varieties of free groups, Moduli spaces of stable pairs and non-abelian zeta functions of curves via wall-crossing, Quiver bundles and wall crossing for chains, Birationality of moduli spaces of twisted \(\mathrm {U}(p,q)\)-Higgs bundles, BPS states, torus links and wild character varieties, On the motives of moduli of chains and Higgs bundles, Indecomposable vector bundles and stable Higgs bundles over smooth projective curves, Counting Higgs bundles and type quiver bundles, Simpson filtration and oper stratum conjecture

Cites Work

• Unnamed Item
• The fundamental lemma for Lie algebras
• Mixed Hodge polynomials of character varieties. With an appendix by Nicholas M. Katz.
• Mirror symmetry, Langlands duality, and the Hitchin system
• Moduli for decorated tuples of sheaves and representation spaces for quivers
• Moduli problems of sheaves associated with oriented trees
• On the motives of moduli of chains and Higgs bundles
• A note of functional equations for zeta functions with values in Chow motives
• DIMENSIONAL REDUCTION, ${\rm SL} (2, {\mathbb C})$-EQUIVARIANT BUNDLES AND STABLE HOLOMORPHIC CHAINS
• Harmonic Bundles on Noncompact Curves
• On the geometry of moduli spaces of holomorphic chains over compact Riemann surfaces
• The Self-Duality Equations on a Riemann Surface