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Betti Numbers of parabolic U(2,1)-Higgs bundles moduli spaces

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Let X be a compact Riemann surface together with a finite set of marked points. We use Morse theoretic techniques to compute the Betti numbers of the parabolic U(2,1)-Higgs bundles moduli spaces over X. We give examples for one marked point showing that the Poincaré polynomials depend on the system of weights of the parabolic bundle.

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  1. Atiyah M.F. and Bott R. (1982). The Yang-Mills equations over Riemann surfaces. Philos. Trans. R. Soc. Lond. 308: 523–615

    MathSciNet  Google Scholar 

  2. Álvarez-Cónsul, L., García-Prada,O., Schmitt, A.H.W.: On the geometry of moduli spaces of holomorphic chains over compact Riemann surfaces. To appear in Int. Math. Res. Pap. Vol. 2006

  3. Boden H.U. and Yokogawa K. (1996). Moduli spaces of parabolic Higgs bundles and parabolic K(D) pairs over smooth curves. I. Int. J. Math. 7: 573–598

    MATH  MathSciNet  Google Scholar 

  4. Frankel T. (1959). Fixed points and torsion on Kähler manifolds. Ann. Math. 70: 1–8

    MathSciNet  Google Scholar 

  5. García-Prada, O., Gothen P.B., Muñoz, V.: Betti numbers of the Moduli space of rank 3 parabolic Higgs bundles, to appear in Mem. Am. Math. Soc.

  6. García-Prada, O., Logares, M., Muñoz, V.: Connected components of the moduli of U(p,q) parabolic Higgs bundles. Preprint (2006), avaliable at

  7. Macdonald I.G. (1962). Symmetric products of an algebraic curve. Topology 1: 319–343

    Article  MATH  MathSciNet  Google Scholar 

  8. Simpson C. (1990). Harmonic bundles on non compact curves. J. Am. Math. Soc. 3: 713–770

    Article  MATH  MathSciNet  Google Scholar 

  9. Thaddeus M. (2002). Variation of moduli of parabolic Higgs bundles. J. Reigne Angew. Math. 547: 1–14

    MATH  MathSciNet  Google Scholar 

  10. Yokogawa K. (1995). Infinitesimal deformation of parabolic Higgs sheaves. Int. J. Math. 6: 125–148

    Article  MATH  MathSciNet  Google Scholar 

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Correspondence to Marina Logares.

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Logares, M. Betti Numbers of parabolic U(2,1)-Higgs bundles moduli spaces. Geom Dedicata 123, 187–200 (2006).

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Mathematics Subject Classification (2000)