Special divisors on real trigonal curves

Abstract In this paper we examine the topology of Brill–Noether varieties associated to real trigonal curves. More precisely, we aim to count the connected components of the real locus of the varieties parametrizing linear systems of degree d and dimension at least r . We do this count when the relations m = g − d + r − 1 ≤ d − 2 r − 1 are satisfied, where m is the Maroni invariant and g is the genus of the curve.