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Geometric Properties of the GIT Quotient

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Part of the Lecture Notes in Mathematics book series (LNM,volume 2122)

Abstract

For any d > 2(2g − 2), consider the open and closed subscheme \(\mathrm{Ch}^{-1}(\mathrm{Chow}_{d}^{\mathit{ss}})^{o}\) of the Chow-semistable locus \(\mathrm{Ch}^{-1}(\mathrm{Chow}_{d}^{\mathit{ss}}) \subset \mathrm{ Hilb}_{d}\) consisting of connected curves, see (10.1). From now on, in order to shorten the notation, we set

$$\displaystyle{ H_{d}:=\mathrm{ Ch}^{-1}(\mathrm{Chow}_{ d}^{\mathit{ss}})^{o} \subset \mathrm{ Hilb}_{ d} }$$
(14.1)

and we call H d the main component of the Chow-semistable locus.

Keywords

  • Iitaka Fibration
  • Moduli Morphism
  • Canonical Singularities
  • Kodaira Dimension
  • Open Subscheme

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Bini, G., Felici, F., Melo, M., Viviani, F. (2014). Geometric Properties of the GIT Quotient. In: Geometric Invariant Theory for Polarized Curves. Lecture Notes in Mathematics, vol 2122. Springer, Cham. https://doi.org/10.1007/978-3-319-11337-1_14

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