Moduli of Curves by Leticia Brambila Paz Ciro Ciliberto Eduardo Esteves Margarida Melo & Claire Voisin

Author:Leticia Brambila Paz, Ciro Ciliberto, Eduardo Esteves, Margarida Melo & Claire Voisin
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

The same filtration argument on the vector bundle M L shows that in the case of curves, the Betti diagram consists of only two rows, namely that of linear syzygies and that of quadratic syzygies respectively.

Proposition 3.6

Let L be a globally generated non-special line bundle L on a smooth curve C. Then K p, q (C, L) = 0 for all q ≥ 3 and all p.

Thus making abstraction of the 0-th row in which the only non-zero entry is b 0,0 = 1, the resolution of each non-special curve C ⊆ P r has the shape shown in Table 1. Table 1The Betti table of a non-special curve of genus g

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