Rationality of moduli space of torsion-free sheaves over reducible curve

Let C be a curve with two smooth components and a single node, and let 𝓤C(w, r, χ) be the moduli space of w-semistable classes of depth one sheaves on C having rank r on both components and Euler characteristic χ. In this paper, under suitable assumptions, we produce a projective bundle over the product of the moduli spaces of semistable vector bundles of rank r on each component and we show that it is birational to an irreducible component of 𝓤C(w, r, χ). Then we prove the rationality of the closed subset containing vector bundles with given fixed determinant.

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Rationality of moduli space of torsion-free sheaves over reducible curve

Cited by 2 publications

References 13 publications

On the rationality of moduli spaces of vector bundles over chain-like curves

On the rationality of moduli spaces of vector bundles over chain-like curves

On vector bundles over reducible curves with a node

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