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Elliptic Tails and Tacnodes with a Line

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

Abstract

According to Corollary 5.6(i), if \([X \subset \mathbb{P}^{r}] \in \mathrm{Hilb}_{d}\) is Chow semistable with X connected and \(2(2g - 2) < d \leq 4(2g - 2)\), then X is quasi-wp-stable. The aim of this chapter is to investigate whether X can have elliptic tails or tacnodes with a line.

Keywords

  • Elliptic Tails
  • Tacnode
  • Previous Theorem
  • Algebraic Geometry

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Fig. 9.1
Fig. 9.2

References

  1. D. Gieseker, Lectures on Moduli of Curves. Tata Institute of Fundamental Research Lectures on Mathematics and Physics, vol. 69 (Tata Institute of Fundamental Research, Bombay, 1982)

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  2. D. Hyeon, I. Morrison, Stability of tails and 4-canonical models. Math. Res. Lett. 17(4), 721–729 (2010)

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© 2014 Springer International Publishing Switzerland

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Bini, G., Felici, F., Melo, M., Viviani, F. (2014). Elliptic Tails and Tacnodes with a Line. 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_9

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