Abstract
One of the first successful applications of Geometric Invariant Theory (GIT for short), and perhaps one of the major motivations for its development by Mumford and his co-authors (see [MFK94]), was the construction of the moduli space M g of smooth curves of genus g ≥ 2 and its compactification \(\overline{M}_{g}\) via stable curves (i.e. connected nodal projective curves with finite automorphism group), carried out by Mumford [Mum77] and Gieseker [Gie82].
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Notes
- 1.
Notice that Li-Wang worked more generally with polarized pointed weighted nodal curves.
- 2.
In particular, when working with Hilb d , we will always consider the m-linearization for m ≫ 0; see Sect. 4.1 for details.
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Bini, G., Felici, F., Melo, M., Viviani, F. (2014). Introduction. 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_1
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