Real Algebraic and Analytic Geometry
Submission: 2003, January 15.
In the first part, we study effective divisors on a smooth projective curve over the field of real numbers, with totally real or totally complex support. We give some numerical conditions for a linear system to contain such a divisor. In the second part, we describe the special linear systems on a real hyperelliptic curve and prove a new Clifford inequality for such curves. Finally, we study the existence of complete linear systems of small degrees and dimension $r$ on a real curve.
Mathematics Subject Classification (2000): 14C20, 14H51, 14P25, 14P99.
Keywords and Phrases: real curve, special linear system, Brill-Noether theory, Jacobian variety.
Full text, 22p.: dvi 94k, ps.gz 75k, pdf 210k.