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].

Linear series on semistable curves

CAPORASO, Lucia
2010-01-01

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.
Caporaso, L. (2010). Linear series on semistable curves. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 49 [10.1093/imrn/rnq188].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11590/137053
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