Relative Geometric Invariant Theory and Universal Moduli Spaces

1995/04/25 by Yi Hu, Hu, Yi
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #alg-geom #math.AG

paper · pdf · doi:10.48550/arxiv.alg-geom/9504014

31 pages, AMSLaTeX

arxiv created 1995/04/25 · arxiv updated 2009/11/30

Abstract

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 M_g of Simpson's p-semistable coherent sheaves and a canonical dominating morphism from the universal Hilbert scheme over M_g to a compactified universal Picard.

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