Real Algebraic and Analytic Geometry
Submission: 2003, November 13.
In this note, we study effective Cartier divisors with totally real or totally complex supports on a projective curve over IR. We give some numerical conditions for an invertible sheaf to be isomorphic or not to such a divisor. We show that these conditions are strongly related to the singularities of the curve and to topological properties of the real part of the Jacobian variety.
Mathematics Subject Classification (1991): 14C20, 14H51, 14P25, 14P99.
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