Relative Geometric Invariant Theory and Universal Moduli Spaces

Details Relative Geometric Invariant Theory and Universal Moduli Spaces Relative Geometric Invariant Theory and Universal Moduli Spaces

1995-04-25

arxiv.org/abs/alg-geom/9504014v1

Mathematics

Algebraic Geometry

31 pages, AMSLaTeX

Scientific paper

We expose in detail the principle that the relative geometric invariant theory of equivariant morphisms is related to the GIT for linearizations near the boundary of the $G$-effective ample cone. We then apply this principle to construct and reconstruct various universal moduli spaces. In particular, we constructed the universal moduli space over $\overline{M_g}$ of Simpson's $p$-semistable coherent sheaves and a canonical dominating morphism from the universal Hilbert scheme over $\overline{M_g}$ to a compactified universal Picard.

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