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On dimension theorems of the varieties of special divisors on a curve

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Abbreviations

ℕ0 :

ℕ∪{0}

X :

a smooth irreducible projective curve overℂ of genusp>0

J :

the Jacobian variety ofX

W νr :

the image of all effective divisorsD ofX of degree deg(D)=r and dimensionh(D)≧v(r,v∈ℕ), under the Jacobian homomorphism of the divisor group ofX ontoJ

W r :

W 1r

X νr :

W νr /(W νr−1 +W 1) (whereW νr−1 +W 1=∅ ifW νr−1 =∅)

g ν−1r :

a complete linear series onX, of degreer, and (projective) dimension ν−1

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Authors and Affiliations

  1. Mathematisches Institut der Universität, D-8520, Erlangen, Federal Republic of Germany

    G. Martens

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  1. G. Martens
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Martens, G. On dimension theorems of the varieties of special divisors on a curve. Math. Ann. 267, 279–288 (1984). https://doi.org/10.1007/BF01579204

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  • DOI: https://doi.org/10.1007/BF01579204

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