On moduli spaces of Hitchin pairs
2011 ◽
Vol 151
(3)
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pp. 441-457
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AbstractLetXbe a compact Riemann surfaceXof genus at–least two. Fix a holomorphic line bundleLoverX. Letbe the moduli space of Hitchin pairs (E, φ ∈H0(End0(E) ⊗L)) overXof rankrand fixed determinant of degreed. The following conditions are imposed:(i)deg(L) ≥ 2g−2,r≥ 2, andL⊗rKX⊗r;(ii)(r, d) = 1; and(iii)ifg= 2 thenr≥ 6, and ifg= 3 thenr≥ 4.We prove that that the isomorphism class of the varietyuniquely determines the isomorphism class of the Riemann surfaceX. Moreover, our analysis shows thatis irreducible (this result holds without the additional hypothesis on the rank for low genus).
2010 ◽
Vol 21
(04)
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pp. 497-522
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1999 ◽
Vol 66
(1)
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pp. 32-50
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2001 ◽
Vol 63
(3)
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pp. 754-768
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2017 ◽
Vol 14
(10)
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pp. 1750144
Keyword(s):
2017 ◽
Vol 107
(9)
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pp. 1581-1589
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2018 ◽
Vol 15
(05)
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pp. 1850081
Keyword(s):
2004 ◽
Vol 76
(3)
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pp. 415-424