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Extra Components of the GIT Quotient

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

Abstract

So far, we have considered the action of \(\mathrm{GL}_{r+1}\) over Hilb d , and we have restricted our attention to \(\mathrm{Ch}^{-1}(\mathrm{Chow}_{d}^{\mathit{ss}})^{o}\) and \(\mathrm{Hilb}_{d}^{\mathit{ss},o}\), the Chow or Hilbert semistable loci consisting of connected curves. It is very natural to ask if there are Chow or Hilbert semistable points \([X \subset \mathbb{P}^{r}] \in \mathrm{ Hilb}_{d}\) with X not connected. In this chapter we will answer this question.

Keywords

  • Extra Components
  • Local Semantics
  • Line Bundle
  • Previous Corollary
  • Smooth Curve

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© 2014 Springer International Publishing Switzerland

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Bini, G., Felici, F., Melo, M., Viviani, F. (2014). Extra Components 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_15

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