American Institute of Mathematical Sciences

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  2013, 20: 103-108. doi: 10.3934/era.2013.20.105

On degenerations of moduli of Hitchin pairs

V. Balaji 1, , P. Barik 1, and  D. S. Nagaraj 2,

1. 

Chennai Mathematical Institute SIPCOT IT Park, Siruseri-603103, India, India
2. 

Institute of Mathematical Sciences, Taramani, Chennai-600115, India

Received  May 2013 Revised  September 2013 Published  December 2013

The purpose of this note is to announce certain basic results on the construction of a degeneration of ${\mathcal{M}}_{{{X_{k}}}}^{{H}}(n,d)$ as the smooth curve $X_{k}$ degenerates to an irreducible nodal curve with a single node.
Keywords: Picard varieties, nodal curves, Hitchin triples, Hitchin pairs.
Citation: V. Balaji, P. Barik, D. S. Nagaraj. On degenerations of moduli of Hitchin pairs. Electronic Research Announcements, 2013, 20: 103-108. doi: 10.3934/era.2013.20.105
References:
[1]

V. Balaji, P. Barik and D. S. Nagaraj, A degeneration of the moduli of Hitchin pairs,, \arXiv{1308.4490}., ().   Google Scholar

[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.  Google Scholar

[3]

D. Gieseker, A degeneration of the moduli space of stable bundles, J. Differential Geom., 19 (1984), 173-206.  Google Scholar

[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.  Google Scholar

[5]

N. J. Hitchin, Stable bundles and integrable systems, Duke Math. J., 54 (1987), 91-114. doi: 10.1215/S0012-7094-87-05408-1.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[9]

C. Procesi, The toric variety associated to Weyl chambers, in Mots, Lang. Raison. Calc., Hermès, Paris, 1990, 153-161.  Google Scholar

[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.  Google Scholar

[11]

C. Simpson, Higgs bundles and local systems, Inst. Hautes Études Sci. Publ. Math., 75 (1992), 5-95.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

show all references

References:
[1]

V. Balaji, P. Barik and D. S. Nagaraj, A degeneration of the moduli of Hitchin pairs,, \arXiv{1308.4490}., ().   Google Scholar

[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.  Google Scholar

[3]

D. Gieseker, A degeneration of the moduli space of stable bundles, J. Differential Geom., 19 (1984), 173-206.  Google Scholar

[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.  Google Scholar

[5]

N. J. Hitchin, Stable bundles and integrable systems, Duke Math. J., 54 (1987), 91-114. doi: 10.1215/S0012-7094-87-05408-1.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[9]

C. Procesi, The toric variety associated to Weyl chambers, in Mots, Lang. Raison. Calc., Hermès, Paris, 1990, 153-161.  Google Scholar

[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.  Google Scholar

[11]

C. Simpson, Higgs bundles and local systems, Inst. Hautes Études Sci. Publ. Math., 75 (1992), 5-95.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

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