Pubblicato
Stabilization of the Homotopy Groups of the Moduli Spaces of k-Higgs Bundles
Estabilización de los Grupos de Homotopía de los Espacios Móduli de los k-Fibrados de Higgs
DOI:
https://doi.org/10.15446/recolma.v1n52.74525Parole chiave:
Moduli of Higgs Bundles, Variations of Hodge Structures, Vector Bundles (en)Moduli de Fibrados de Higgs, Variaciones de Estructuras de Hodge, Fibrados Vectoriales (es)
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Riferimenti bibliografici
M. F. Atiyah, Vector Bundles and Künneth Formula, Topology 1 (1962),
-248.
M. F. Atiyah, K-Theory, W. A. Benjamin, New York-Amsterdam, 1967.
M. F. Atiyah and R. Bott, Yang-Mills equations over Riemann surfaces,
Phil. Trans. Roy. Soc. London A 308 (1982), 523-615.
S. Bento, Topologia do Espaco Moduli de Fibrados de Higgs Torcidos, Tese de Doutoramento, Universidade do Porto, Porto, Portugal, 2010.
S. B. Bradlow and O. García-Prada, Stable triples, equivariant bundles and dimensional reduction, Math. Ann. 304 (1996), 225-252.
S. B. Bradlow, O. García-Prada, and P. B. Gothen, Moduli spaces of holomorphic triples over compact Riemann surfaces, Math. Ann. 328 (2004), 299-351.
S. B. Bradlow, O. García-Prada, and P. B. Gothen, Homotopy groups of moduli spaces of representations, Topology 47 (2008), 203-224.
T. Frankel, Fixed points and torsion on Kähler manifolds, Ann. Math. 70
(1959), 1-8.
W. Fulton, Algebraic Topology, A First Course, Springer, New York, 1995.
P. B. Gothen, The Betti numbers of the moduli space of stable rank 3 Higgs bundles on a Riemann surface, Int. J. Math. 5 (1994), no. 1, 861-875.
P. B. Gothen and R. A. Zúñiga-Rojas, Stratifications on the moduli space of Higgs bundles, Portugaliae Mathematica, to appear.
P. Griffiths and J. Harris, Principles of Algebraic Geometry, Wiley, New
York, 1978.
A. Hatcher, Algebraic Topology, Cambridge University Press, Cambridge, 2002.
T. Hausel, Geometry of the moduli space of Higgs bundles, Ph. D. thesis, Cambridge, 1998.
T. Hausel and M. Thaddeus, Mirror symmetry, Langlads duality, and the Hitchin system, Invent. Math. 153 (2003), 197-229.
T. Hausel and M. Thaddeus, Generators for the cohomology ring of the moduli space of rank 2 Higgs bundles, Proc. London Math. Soc. 88 (2004), 632-658.
N. J. Hitchin, The self-duality equations on a Riemann surface, Proc. London Math. Soc. 55 (1987), 59-126.
D. Husemoller, Fibre Bundles, third edition, Graduate Texts in Mathematics 20, Springer, New York, 1994.
I. M. James and ed., Handbook of Algebraic Topology, (1995).
I. G. Macdonald, Symmetric products of an algebraic curve, Topology 1
(1962), 319-343.
E. Markman, Integral generators for the cohomology ring of moduli spaces of sheaves over Poisson surfaces, Adv. Math. 208 (2007), 622-646.
V. Muñoz, D. Ortega, and M. J. Vázquez-Gallo, Hodge polynomials of the moduli spaces of pairs, Int. J. Math. 18 (2007), 695-721.
N. Nitsure, Moduli space of semistable pairs on a curve, Proc. London
Math. Soc. 62 (1991), 275-300.
C. T. Simpson, Constructing variations of Hodge structures using Yang{
Mills theory and applications to uniformization, J. Amer. Math. Soc. 1
(1988), 867-918.
, Higgs bundles and local systems, Publ. Math. IHÉS (1992), 5-95.
R. A. Zúñiga-Rojas, Homotopy groups of the moduli space of Higgs bundles, Ph. D. thesis, Porto, Portugal, 2015.
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1. Alfonso Zamora Saiz, Ronald A. Zúñiga-Rojas. (2021). Geometric Invariant Theory, Holomorphic Vector Bundles and the Harder-Narasimhan Filtration. SpringerBriefs in Mathematics. , p.101. https://doi.org/10.1007/978-3-030-67829-6_6.
2. Alfonso Zamora Saiz, Ronald A. Zúñiga-Rojas. (2021). Geometric Invariant Theory, Holomorphic Vector Bundles and the Harder-Narasimhan Filtration. SpringerBriefs in Mathematics. , p.1. https://doi.org/10.1007/978-3-030-67829-6_1.
3. Ronald A. Zúñiga-Rojas. (2021). Variations of hodge structures of rank three k-Higgs bundles and moduli spaces of holomorphic triples. Geometriae Dedicata, 213(1), p.137. https://doi.org/10.1007/s10711-020-00572-0.
4. David Alfaya, André Oliveira. (2024). Lie algebroid connections, twisted Higgs bundles and motives of moduli spaces. Journal of Geometry and Physics, 201, p.105195. https://doi.org/10.1016/j.geomphys.2024.105195.
5. Peter B. Gothen, Ronald A. Zúñiga-Rojas. (2022). Stratifications on the nilpotent cone of the moduli space of Hitchin pairs. Revista Matemática Complutense, 35(2), p.311. https://doi.org/10.1007/s13163-021-00400-3.
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