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Variety of Special Nets of Degree g-1 on Double Coverings of a Smooth Plane Quartic of Genus 9

  • Kyung-Hye Cho
  • Changho Keem
  • Akira Ohbuchi
Part of the International Society for Analysis, Applications and Computation book series (ISAA, volume 8)

Abstract

Let C be a complete non-singular curve over ℂ of genus g. We denote by W d r (C) the subscheme of the Picard variety Pic d (C) whose support is the locus of complete linear series of degree d and dimension at least r. In case d > g + r - 1, W d r (C) = Pic d (C) and if d = g + r - 1, W d r (C) has dimension d. Therefore the dimension of W d r (C) is independent of C in the range dg + r - 1. If dg + r - 2, one knows that dimW d r (C) ≥ p(d, g, r):= g - (r + 1) (g - d + r) for any curve C and is equal to p(d, g, r) for general curve C (see Kleiman-Laksov [9] and Griffiths-Harris [6]). But the dimension of W d r (C) might be greater than p(d, g, r) for some special curve C. Moreover, for curves C with dim W d r (C) > p(d, g, r), C must be of some special type of curves. The first important result along this line is the following well-known theorem of H. Martens which has been extended by a theorem of D. Mumford.

Keywords

Singular Point Exact Sequence Irreducible Component Double Covering Algebraic Curve 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • Kyung-Hye Cho
    • 1
  • Changho Keem
    • 1
  • Akira Ohbuchi
    • 2
  1. 1.Department of MathematicsSeoul National UniversitySeoulKorea
  2. 2.Department of Mathematics, Faculty of Integrated Arts and SciencesTokushima UniversityTokushimaJapan

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