Brauer Group and Birational Type of Moduli Spaces of Torsionfree Sheaves on a Nodal Curve

Abstract

Let U s n d be the moduli space of stable vector bundles of rank n and fixed determinant of degree d on a nodal curve Y . The moduli space of semistable vector bundles of rank n and degree d will be denoted by U Y n d . We calculate the Brauer groups of U s n d . We study the question of rationality of U s n d and U Y n d .

On the rationality of Nagaraj–Seshadri moduli space

“…It is still not known if the moduli space is rational or not in the non-coprime case, even for rank 2 and degree 0. In the non-smooth case, when the curve is irreducible and has any number of nodal singularities and genus ≥ 2, rationality in the coprime case was proved by Bhosle and Biswas [2,Theorem 3.7]. Over a reducible nodal curve X as described above it has been shown by Basu that each irreducible component of M(2, a, χ, ξ) is unirational [1,Lemma 2.5].…”

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

“…It is still not known if the moduli space is rational or not in the non-coprime case, even for rank 2 and degree 0. In the non-smooth case, when the curve is irreducible and has any number of nodal singularities and genus ≥ 2, rationality in the coprime case was proved by Bhosle and Biswas [3,Theorem 3.7]. Over a reducible nodal curve with two components (i.e.…”