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

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

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.
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}., ().

[2]

L. Caporaso, A compactification of the universal Picard variety over the moduli space of stable curves,, \emph{J. Amer. Math. Soc.}, 7 (1994), 589. doi: 10.1090/S0894-0347-1994-1254134-8.

[3]

D. Gieseker, A degeneration of the moduli space of stable bundles,, \emph{J. Differential Geom.}, 19 (1984), 173.

[4]

N. J. Hitchin, The self-duality equations on a Riemann surface,, \emph{Proc. London Math. Soc. (3)}, 55 (1987), 59. doi: 10.1112/plms/s3-55.1.59.

[5]

N. J. Hitchin, Stable bundles and integrable systems,, \emph{Duke Math. J.}, 54 (1987), 91. doi: 10.1215/S0012-7094-87-05408-1.

[6]

I. Kausz, A Gieseker type degeneration of moduli stacks of vector bundles on curves,, \emph{Trans. Amer. Math. Soc.}, 357 (2005), 4897. 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,, \emph{Proc. Indian Acad. Sci. Math. Sci.}, 109 (1999), 165. doi: 10.1007/BF02841533.

[8]

N. Nitsure, Moduli space of semistable pairs on a curve,, \emph{Proc. London Math. Soc. (3)}, 62 (1991), 275. doi: 10.1112/plms/s3-62.2.275.

[9]

C. Procesi, The toric variety associated to Weyl chambers,, in \emph{Mots}, (1990), 153.

[10]

A. Schmitt, The Hilbert compactification of the universal moduli space of semistable vector bundles over smooth curves,, \emph{J. Differential Geom.}, 66 (2004), 169.

[11]

C. Simpson, Higgs bundles and local systems,, \emph{Inst. Hautes Études Sci. Publ. Math.}, 75 (1992), 5.

[12]

C. Simpson, Moduli of representations of the fundamental group of a smooth projective variety. I,, \emph{Inst. Hautes Études Sci. Publ. Math.}, 79 (1994), 47.

[13]

C. Simpson, Moduli of representations of the fundamental group of a smooth projective variety. II,, \emph{Inst. Hautes Études Sci. Publ. Math.}, 80 (1994), 5.

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,, \emph{J. Amer. Math. Soc.}, 7 (1994), 589. doi: 10.1090/S0894-0347-1994-1254134-8.

[3]

D. Gieseker, A degeneration of the moduli space of stable bundles,, \emph{J. Differential Geom.}, 19 (1984), 173.

[4]

N. J. Hitchin, The self-duality equations on a Riemann surface,, \emph{Proc. London Math. Soc. (3)}, 55 (1987), 59. doi: 10.1112/plms/s3-55.1.59.

[5]

N. J. Hitchin, Stable bundles and integrable systems,, \emph{Duke Math. J.}, 54 (1987), 91. doi: 10.1215/S0012-7094-87-05408-1.

[6]

I. Kausz, A Gieseker type degeneration of moduli stacks of vector bundles on curves,, \emph{Trans. Amer. Math. Soc.}, 357 (2005), 4897. 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,, \emph{Proc. Indian Acad. Sci. Math. Sci.}, 109 (1999), 165. doi: 10.1007/BF02841533.

[8]

N. Nitsure, Moduli space of semistable pairs on a curve,, \emph{Proc. London Math. Soc. (3)}, 62 (1991), 275. doi: 10.1112/plms/s3-62.2.275.

[9]

C. Procesi, The toric variety associated to Weyl chambers,, in \emph{Mots}, (1990), 153.

[10]

A. Schmitt, The Hilbert compactification of the universal moduli space of semistable vector bundles over smooth curves,, \emph{J. Differential Geom.}, 66 (2004), 169.

[11]

C. Simpson, Higgs bundles and local systems,, \emph{Inst. Hautes Études Sci. Publ. Math.}, 75 (1992), 5.

[12]

C. Simpson, Moduli of representations of the fundamental group of a smooth projective variety. I,, \emph{Inst. Hautes Études Sci. Publ. Math.}, 79 (1994), 47.

[13]

C. Simpson, Moduli of representations of the fundamental group of a smooth projective variety. II,, \emph{Inst. Hautes Études Sci. Publ. Math.}, 80 (1994), 5.

[1]

Yvette Kosmann-Schwarzbach. Dirac pairs. Journal of Geometric Mechanics, 2012, 4 (2) : 165-180. doi: 10.3934/jgm.2012.4.165

[2]

V. Kumar Murty, Ying Zong. Splitting of abelian varieties. Advances in Mathematics of Communications, 2014, 8 (4) : 511-519. doi: 10.3934/amc.2014.8.511

[3]

Katarzyna Grabowska, Luca Vitagliano. Tulczyjew triples in higher derivative field theory. Journal of Geometric Mechanics, 2015, 7 (1) : 1-33. doi: 10.3934/jgm.2015.7.1

[4]

Katarzyna Grabowska, Janusz Grabowski. Tulczyjew triples: From statics to field theory. Journal of Geometric Mechanics, 2013, 5 (4) : 445-472. doi: 10.3934/jgm.2013.5.445

[5]

Chi-Kwong Fok. Picard group of isotropic realizations of twisted Poisson manifolds. Journal of Geometric Mechanics, 2016, 8 (2) : 179-197. doi: 10.3934/jgm.2016003

[6]

Darryl D. Holm, Cornelia Vizman. Dual pairs in resonances. Journal of Geometric Mechanics, 2012, 4 (3) : 297-311. doi: 10.3934/jgm.2012.4.297

[7]

G. Mashevitzky, B. Plotkin and E. Plotkin. Automorphisms of categories of free algebras of varieties. Electronic Research Announcements, 2002, 8: 1-10.

[8]

A. Giambruno and M. Zaicev. Minimal varieties of algebras of exponential growth. Electronic Research Announcements, 2000, 6: 40-44.

[9]

Laurenţiu Maxim, Jörg Schürmann. Characteristic classes of singular toric varieties. Electronic Research Announcements, 2013, 20: 109-120. doi: 10.3934/era.2013.20.109

[10]

Aravind Asok, James Parson. Equivariant sheaves on some spherical varieties. Electronic Research Announcements, 2011, 18: 119-130. doi: 10.3934/era.2011.18.119

[11]

Anton Izosimov. Pentagrams, inscribed polygons, and Prym varieties. Electronic Research Announcements, 2016, 23: 25-40. doi: 10.3934/era.2016.23.004

[12]

Peter K. Friz, I. Kukavica, James C. Robinson. Nodal parametrisation of analytic attractors. Discrete & Continuous Dynamical Systems - A, 2001, 7 (3) : 643-657. doi: 10.3934/dcds.2001.7.643

[13]

Yong Lin, Gábor Lippner, Dan Mangoubi, Shing-Tung Yau. Nodal geometry of graphs on surfaces. Discrete & Continuous Dynamical Systems - A, 2010, 28 (3) : 1291-1298. doi: 10.3934/dcds.2010.28.1291

[14]

Kevin Kuo, Phong Luu, Duy Nguyen, Eric Perkerson, Katherine Thompson, Qing Zhang. Pairs trading: An optimal selling rule. Mathematical Control & Related Fields, 2015, 5 (3) : 489-499. doi: 10.3934/mcrf.2015.5.489

[15]

R.D.S. Oliveira, F. Tari. On pairs of differential $1$-forms in the plane. Discrete & Continuous Dynamical Systems - A, 2000, 6 (3) : 519-536. doi: 10.3934/dcds.2000.6.519

[16]

Shahar Nevo, Xuecheng Pang and Lawrence Zalcman. Picard-Hayman behavior of derivatives of meromorphic functions with multiple zeros. Electronic Research Announcements, 2006, 12: 37-43.

[17]

Primitivo B. Acosta-Humánez, J. Tomás Lázaro, Juan J. Morales-Ruiz, Chara Pantazi. On the integrability of polynomial vector fields in the plane by means of Picard-Vessiot theory. Discrete & Continuous Dynamical Systems - A, 2015, 35 (5) : 1767-1800. doi: 10.3934/dcds.2015.35.1767

[18]

Jesús Carrillo-Pacheco, Felipe Zaldivar. On codes over FFN$(1,q)$-projective varieties. Advances in Mathematics of Communications, 2016, 10 (2) : 209-220. doi: 10.3934/amc.2016001

[19]

Sylvain E. Cappell, Anatoly Libgober, Laurentiu Maxim and Julius L. Shaneson. Hodge genera and characteristic classes of complex algebraic varieties. Electronic Research Announcements, 2008, 15: 1-7. doi: 10.3934/era.2008.15.1

[20]

Bernard Helffer, Thomas Hoffmann-Ostenhof, Susanna Terracini. Nodal minimal partitions in dimension $3$. Discrete & Continuous Dynamical Systems - A, 2010, 28 (2) : 617-635. doi: 10.3934/dcds.2010.28.617

2016 Impact Factor: 0.483

Metrics

  • PDF downloads (2)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]