Master Spaces for stable pairs

Details Master Spaces for stable pairs Master Spaces for stable pairs

1996-07-17

arxiv.org/abs/alg-geom/9607015v2

Physics

High Energy Physics

High Energy Physics - Theory

26 pages. New introduction and applications LaTeX2e

Scientific paper

We construct master spaces for oriented torsion free sheaves coupled with morphisms into a fixed reference sheaf. These spaces are projective varieties endowed with a natural $\C^*$-action. The fixed point set of this action contains the moduli space of semistable oriented torsion free sheaves and the quot scheme associated with the given data. In the case of curves with trivial reference sheaf, our master spaces compactify the moduli spaces constructed by Bertram, Daskalopoulos and Wentworth. In the 2-dimensional case with trivial rank 1 reference sheaf, master spaces provide algebraic analoga of compactified moduli spaces of twisted quaternionic monopoles.

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