Complete Linear Series on a Hyperelliptic Curve

2008/08/01 by Euisung Park, Park, Euisung
Mathematics · Physics and Astronomy · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.0808.0113

Abstract

In this paper we study complete linear series on a hyperelliptic curve C of arithmetic genus g. Let A be the unique line bundle on C such that |A| is a g¹₂, and let L be a line bundle on C of degree d. Then L can be factorized as L = A^m ⊗ B where m is the largest integer satisfying H⁰ (C,L ⊗ A^-m) ≠ 0. Let b = deg(B). We say that the factorization type of L is (m,b). Our main results in this paper assert that (m,b) gives a precise answer for many natural questions about L.

Citations

• On the projective normality of complete linear series on an algebraic curve

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