Author:

Keywords:

real curve, linear system, Science & Technology, Physical Sciences, Mathematics, Real curve, totally non-real divisor, 0101 Pure Mathematics, General Mathematics, 4904 Pure mathematics

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.