Abstract
The aim of this Appendix is to investigate positivity properties of balanced line bundles of sufficiently high degree on (reduced) Gorenstein curves. The results obtained here are applied in this manuscript only for quasi-wp-stable curves; however we decided to present these results in the Gorenstein case for two reasons: firstly, we think that these results are interesting in their own (in particular we will generalize our proofs extend without any modifications to the Gorenstein case.
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Notes
- 1.
The letter G stands for Gorenstein to suggest that these notions are the natural generalizations of the usual notions from nodal to Gorenstein curves.
- 2.
Note that a subcurve of a Gorenstein curve need not to be Gorenstein. For example, the curve X given by the union of 4 generic lines through the origin in \(\mathbb{A}_{k}^{3}\) is Gorenstein, but each subcurve of X given by the union of three lines is not Gorenstein.
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Bini, G., Felici, F., Melo, M., Viviani, F. (2014). Appendix: Positivity Properties of Balanced Line Bundles. 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_17
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