Real Algebraic and Analytic Geometry |

Divisors on real curves.

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Submission: 2003, January 15.

*Abstract:
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.:
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