Rationality of the moduli space of stable pairs over a complex curve
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2012
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Springer
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Biswas, I., Logares Jiménez, M. L. & Muñoz Velázquez, V. «Rationality of the Moduli Space of Stable Pairs over a Complex Curve». Nonlinear Analysis, editado por Panos M. Pardalos et al., vol. 68, Springer New York, 2012, pp. 65-77. DOI.org (Crossref), https://doi.org/10.1007/978-1-4614-3498-6_5.
Abstract
Let X be a smooth complex projective curve of genus g≥2. A pair on X is formed by a vector bundle E→X and a global non-zero section ϕ∈H 0(E). There is a concept of stability for pairs depending on a real parameter τ, giving rise to moduli spaces of τ-stable pairs of rank r and fixed determinant Λ. In this paper, we prove that the moduli spaces are in many cases rational.
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Dedicated to the 60th Anniversary of Themistocles M. Rassias