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Area preserving maps on $\boldsymbol{S^2}$: A lower bound on the $\boldsymbol{C^0}$-norm using symplectic spectral invariants
On degenerations of moduli of Hitchin pairs
1. | Chennai Mathematical Institute SIPCOT IT Park, Siruseri-603103, India, India |
2. | Institute of Mathematical Sciences, Taramani, Chennai-600115, India |
References:
[1] |
V. Balaji, P. Barik and D. S. Nagaraj, A degeneration of the moduli of Hitchin pairs, arXiv:1308.4490. |
[2] |
L. Caporaso, A compactification of the universal Picard variety over the moduli space of stable curves, J. Amer. Math. Soc., 7 (1994), 589-660.
doi: 10.1090/S0894-0347-1994-1254134-8. |
[3] |
D. Gieseker, A degeneration of the moduli space of stable bundles, J. Differential Geom., 19 (1984), 173-206. |
[4] |
N. J. Hitchin, The self-duality equations on a Riemann surface, Proc. London Math. Soc. (3), 55 (1987), 59-126.
doi: 10.1112/plms/s3-55.1.59. |
[5] |
N. J. Hitchin, Stable bundles and integrable systems, Duke Math. J., 54 (1987), 91-114.
doi: 10.1215/S0012-7094-87-05408-1. |
[6] |
I. Kausz, A Gieseker type degeneration of moduli stacks of vector bundles on curves, Trans. Amer. Math. Soc., 357 (2005), 4897-4955.
doi: 10.1090/S0002-9947-04-03618-9. |
[7] |
D. S. Nagaraj and C. S. Seshadri, Degenerations of the moduli spaces of vector bundles on curves. II. Generalized Gieseker moduli spaces, Proc. Indian Acad. Sci. Math. Sci., 109 (1999), 165-201.
doi: 10.1007/BF02841533. |
[8] |
N. Nitsure, Moduli space of semistable pairs on a curve, Proc. London Math. Soc. (3), 62 (1991), 275-300.
doi: 10.1112/plms/s3-62.2.275. |
[9] |
C. Procesi, The toric variety associated to Weyl chambers, in Mots, Lang. Raison. Calc., Hermès, Paris, 1990, 153-161. |
[10] |
A. Schmitt, The Hilbert compactification of the universal moduli space of semistable vector bundles over smooth curves, J. Differential Geom., 66 (2004), 169-209. |
[11] |
C. Simpson, Higgs bundles and local systems, Inst. Hautes Études Sci. Publ. Math., 75 (1992), 5-95. |
[12] |
C. Simpson, Moduli of representations of the fundamental group of a smooth projective variety. I, Inst. Hautes Études Sci. Publ. Math., 79 (1994), 47-129. |
[13] |
C. Simpson, Moduli of representations of the fundamental group of a smooth projective variety. II, Inst. Hautes Études Sci. Publ. Math., 80 (1994), 5-79. |
show all references
References:
[1] |
V. Balaji, P. Barik and D. S. Nagaraj, A degeneration of the moduli of Hitchin pairs, arXiv:1308.4490. |
[2] |
L. Caporaso, A compactification of the universal Picard variety over the moduli space of stable curves, J. Amer. Math. Soc., 7 (1994), 589-660.
doi: 10.1090/S0894-0347-1994-1254134-8. |
[3] |
D. Gieseker, A degeneration of the moduli space of stable bundles, J. Differential Geom., 19 (1984), 173-206. |
[4] |
N. J. Hitchin, The self-duality equations on a Riemann surface, Proc. London Math. Soc. (3), 55 (1987), 59-126.
doi: 10.1112/plms/s3-55.1.59. |
[5] |
N. J. Hitchin, Stable bundles and integrable systems, Duke Math. J., 54 (1987), 91-114.
doi: 10.1215/S0012-7094-87-05408-1. |
[6] |
I. Kausz, A Gieseker type degeneration of moduli stacks of vector bundles on curves, Trans. Amer. Math. Soc., 357 (2005), 4897-4955.
doi: 10.1090/S0002-9947-04-03618-9. |
[7] |
D. S. Nagaraj and C. S. Seshadri, Degenerations of the moduli spaces of vector bundles on curves. II. Generalized Gieseker moduli spaces, Proc. Indian Acad. Sci. Math. Sci., 109 (1999), 165-201.
doi: 10.1007/BF02841533. |
[8] |
N. Nitsure, Moduli space of semistable pairs on a curve, Proc. London Math. Soc. (3), 62 (1991), 275-300.
doi: 10.1112/plms/s3-62.2.275. |
[9] |
C. Procesi, The toric variety associated to Weyl chambers, in Mots, Lang. Raison. Calc., Hermès, Paris, 1990, 153-161. |
[10] |
A. Schmitt, The Hilbert compactification of the universal moduli space of semistable vector bundles over smooth curves, J. Differential Geom., 66 (2004), 169-209. |
[11] |
C. Simpson, Higgs bundles and local systems, Inst. Hautes Études Sci. Publ. Math., 75 (1992), 5-95. |
[12] |
C. Simpson, Moduli of representations of the fundamental group of a smooth projective variety. I, Inst. Hautes Études Sci. Publ. Math., 79 (1994), 47-129. |
[13] |
C. Simpson, Moduli of representations of the fundamental group of a smooth projective variety. II, Inst. Hautes Études Sci. Publ. Math., 80 (1994), 5-79. |
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