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Moduli of stable pairs for holomorphic bundles over Riemann surfaces. (English) Zbl 0759.32013
The authors study the space of gauge equivalence classes of pairs \((\overline\partial_ E,\varphi)\) of a holomorphic structure \(\overline\partial_ E\) on a complex bundle \(E\) over a closed Riemann surface and a holomorphic section \(\varphi\). They define a space of stable pairs and consider the moduli space problem for this space. The space of stable pairs is related to the space of solutions of the vortex equation, i.e., Hermitian-Yang-Mills-Higgs equation. Using the parameter \(\tau\) appearing in this equation, they show that, under suitable restrictions on \(\tau\) and the degree of \(E\), the subspace defined by \(\tau\) is naturally a finite dimensional, compact Kähler manifold. Further, they define naturally a holomorphic map from this space on the Seshadri compactification of the moduli space of stable bundles. They show that this map is generically a fibration.

MSC:
32G15 Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables)
32L05 Holomorphic bundles and generalizations
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