Divisors on real curves

Abstract

Let X be a smooth projective curve over R. In the first part, we study eective divi- sors on X 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 sys- tems on a real hyperelliptic curve and prove a new Cliord inequality for such curves. Finally, we study the existence of complete linear systems of small degrees and dimension r on a real curve.