For a semistable curve X of genus g, the number h^0(X, L) is studied for line bundles L of degree d parameterized by the compactified Picard scheme. The theorem of Riemann is shown to hold. The theorem of Clifford is shown to hold in the following cases: X has two components; X is any semistable curve, and d=0 or d=2g − 2; X is stable, free from separating nodes, and d at most 4. These results are shown to be sharp. Applications to the Clifford index, to the combinatorial description of hyperelliptic curves, and to plane quintics are given.
Caporaso L (2010). Linear series on semistable curves. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 49 [10.1093/imrn/rnq188].
Titolo: | Linear series on semistable curves | |
Autori: | ||
Data di pubblicazione: | 2010 | |
Rivista: | ||
Citazione: | Caporaso L (2010). Linear series on semistable curves. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 49 [10.1093/imrn/rnq188]. | |
Abstract: | For a semistable curve X of genus g, the number h^0(X, L) is studied for line bundles L of degree d parameterized by the compactified Picard scheme. The theorem of Riemann is shown to hold. The theorem of Clifford is shown to hold in the following cases: X has two components; X is any semistable curve, and d=0 or d=2g − 2; X is stable, free from separating nodes, and d at most 4. These results are shown to be sharp. Applications to the Clifford index, to the combinatorial description of hyperelliptic curves, and to plane quintics are given. | |
Handle: | http://hdl.handle.net/11590/137053 | |
Appare nelle tipologie: | 1.1 Articolo in rivista |