Excess linear series on an algebraic curve

William Fulton; Joe Harris; Robert Lazarsfeld

doi:10.1090/S0002-9939-1984-0759642-7

Excess linear series on an algebraic curve

William Fulton
, Joe Harris
, Robert Lazarsfeld

Mathematics

Brown University
Harvard University

Research output: Contribution to journal › Article › peer-review

23 Scopus citations

Abstract

We prove that the dimensions of the varieties W^r_d of complete linear series of degree d and dimension at least r on a curve satisfy the inequalities dim W^r_d-1 ≥ dim W^r_d - (r - 1). In particular, a curve with ∞² g¹_d's must have a g¹_d-1.

Original language	English
Pages (from-to)	320-322
Number of pages	3
Journal	Proceedings of the American Mathematical Society
Volume	92
Issue number	3
DOIs	https://doi.org/10.1090/S0002-9939-1984-0759642-7
State	Published - Nov 1984

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title = "Excess linear series on an algebraic curve",

abstract = "We prove that the dimensions of the varieties Wrd of complete linear series of degree d and dimension at least r on a curve satisfy the inequalities dim Wrd-1 ≥ dim Wrd - (r - 1). In particular, a curve with ∞2 g1d's must have a g1d-1.",

author = "William Fulton and Joe Harris and Robert Lazarsfeld",

year = "1984",

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AU - Fulton, William

AU - Harris, Joe

AU - Lazarsfeld, Robert

PY - 1984/11

Y1 - 1984/11

N2 - We prove that the dimensions of the varieties Wrd of complete linear series of degree d and dimension at least r on a curve satisfy the inequalities dim Wrd-1 ≥ dim Wrd - (r - 1). In particular, a curve with ∞2 g1d's must have a g1d-1.

AB - We prove that the dimensions of the varieties Wrd of complete linear series of degree d and dimension at least r on a curve satisfy the inequalities dim Wrd-1 ≥ dim Wrd - (r - 1). In particular, a curve with ∞2 g1d's must have a g1d-1.

UR - https://www.scopus.com/pages/publications/84968518090

U2 - 10.1090/S0002-9939-1984-0759642-7

DO - 10.1090/S0002-9939-1984-0759642-7

M3 - Article

AN - SCOPUS:84968518090

SN - 0002-9939

VL - 92

SP - 320

EP - 322

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 3

ER -

Excess linear series on an algebraic curve

Abstract

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