Rationality of the Moduli Space of Stable Pairs over a Complex Curve

Indranil Biswas (indranil@math.tifr.res.in), Marina Logares (marina.logares@icmat.es) and Vicente Muñoz (vicente.munoz@mat.ucm.es)
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Indranil Biswas: Tata Institute of Fundamental Research
Marina Logares: Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM)
Vicente Muñoz: Universidad Complutense de Madrid

Chapter Chapter 5 in Nonlinear Analysis, 2012, pp 65-77 from Springer

Abstract: 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.

Keywords: Moduli of pairs; Vortex equation; Rationality; Stable rationality; 14D20; 58D27; 14EM20 (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/978-1-4614-3498-6_5

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