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Totally non-real divisors in linear systems on smooth real curves
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Marc Coppens
Published/Copyright:
November 28, 2008
Abstract
Let X be a smooth real curve of genus g ≥ 1 having some real point. Define M(X) as being the smallest integer m such that each line bundle L on X of even degree at least 2m having restrictions of even degree to each connected component of X(ℝ) contains a totally non-real divisor inside |L| (hence a divisor containing no real point of X). In this paper we prove that M(X) = g.
Received: 2007-02-18
Revised: 2007-07-12
Published Online: 2008-11-28
Published in Print: 2008-October
© de Gruyter 2008
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Articles in the same Issue
- Homogeneous geodesics of non-unimodular Lorentzian Lie groups and naturally reductive Lorentzian spaces in dimension three
- Finite type Monge–Ampère foliations
- The horofunction boundary of the Hilbert geometry
- Counting the hyperplane sections with fixed invariants of a plane quintic – three approaches to a classical enumerative problem
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- Covers of Klein surfaces
- A classification of polarized manifolds by the sectional Betti number and the sectional Hodge number
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