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arXiv · alg-geom/9504014

Relative Geometric Invariant Theory and Universal Moduli Spaces

Yi Hu
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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 $\overline{M_g}$ 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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Yi Hu. 1995-04-25. Relative Geometric Invariant Theory and Universal Moduli Spaces. https://arxiv.org/abs/alg-geom/9504014

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