The Beauville-Narasimhan-Ramanan correspondence for twisted Higgs $V$-bundles and components of parabolic $\text{Sp}(2n,\mathbb{R})$-Higgs moduli

We generalize the classical Beauville-Narasimhan-Ramanan correspondence to the case of parabolic Higgs bundles with regular singularities and Higgs $V$-bundles. Using this correspondence along with Bott-Morse theoretic techniques we provide an exact component count for moduli spaces of maximal parabolic $\text{Sp}\left( 2n,\mathbb{R} \right)$-Higgs bundles with fixed parabolic structure.

[1]  Kôji Yokogawa,et al.  INFINITESIMAL DEFORMATION OF PARABOLIC HIGGS SHEAVES , 1995 .

[2]  H. Konno.  Construction of the moduli space of stable parabolic Higgs bundles on a Riemann surface , 1993 .

[3]  V. Munoz,et al.  Betti Numbers of the Moduli Space of Rank 3 Parabolic Higgs Bundles , 2004 .

[4]  S. Rayan,et al.  Twisted argyle quivers and Higgs bundles , 2018, Bulletin des Sciences Mathématiques.

[5]  Oscar Garcia-Prada,et al.  Parabolic Higgs bundles and representations of the fundamental group of a punctured surface into a real group , 2015, Advances in Mathematics.

[6]  David Baraglia,et al.  Monodromy of rank 2 twisted Hitchin systems and real character varieties , 2015, 1506.00372.

[7]  E. Markman.  Spectral curves and integrable systems , 1994 .

[8]  I. Biswas,et al.  An Infinitesimal Study of the Moduli of Hitchin Pairs , 1994 .

[9]  Kôji Yokogawa,et al.  Compactification of moduli of parabolic sheaves and moduli of parabolic Higgs sheaves , 1993 .

[10]  S. Szabó.  The birational geometry of unramified irregular Higgs bundles on curves , 2017 .

[11]  Ben Nasatyr,et al.  Orbifold Riemann surfaces and the Yang-Mills-Higgs equations , 1995, alg-geom/9504015.

[12]  N. Hitchin.  Stable bundles and integrable systems , 1987 .

[13]  N. Hitchin.  THE SELF-DUALITY EQUATIONS ON A RIEMANN SURFACE , 1987 .

[14]  Marina Logares Jiménez,et al.  Parabolic U(p,q)-Higgs bundles , 2006 .

[15]  S. Ramanan,et al.  TWISTED HIGGS BUNDLES AND THE FUNDAMENTAL GROUP OF COMPACT K , 2000, math/0009093.

[16]  Carlos Simpson,et al.  Harmonic bundles on noncompact curves , 1990 .

[17]  Marina Logares,et al.  Moduli spaces of parabolic U(p, q)-higgs bundles , 2006 .

[18]  Indranil Biswas,et al.  On the existence of unitary flat connections over the punctured sphere with given local monodromy around the punctures , 1999 .

[19]  N. Hitchin.  LIE-GROUPS AND TEICHMULLER SPACE , 1992 .

[20]  Hao Sun,et al.  Topological invariants of parabolic G-Higgs bundles , 2018, Mathematische Zeitschrift.

[21]  Michael Groechenig,et al.  Moduli of flat connections in positive characteristic , 2012, 1201.0741.

[22]  Marina Logares,et al.  Moduli of parabolic Higgs bundles and Atiyah algebroids , 2008, 0811.0817.

[23]  Mikio Furuta,et al.  Seifert fibred homology 3-spheres and the Yang-Mills equations on Riemann surfaces with marked points , 1992 .

[24]  Peter Dalakov.  Lectures on Higgs moduli and abelianisation , 2016, 1609.00646.

[25]  M. Narasimhan,et al.  Spectral curves and the generalised theta divisor. , 1989 .

[26]  INDRANIL BISWAS,et al.  PARABOLIC HIGGS BUNDLES AND $\Gamma $-HIGGS BUNDLES , 2013, Journal of the Australian Mathematical Society.

[27]  C. Simpson.  Local Systems on Proper Algebraic V -manifolds , 2010, 1010.3363.