SPIN STRUCTURES AND BRANCH DIVISORS ON p-GONAL RIEMANN SURFACES

摘要

We study spin structures on Riemann and Klein surfaces in terms of divisors. In particular, we take a closer look at spin structures on hyperelliptic and p-gonal surfaces defined by divisors supported on their branch points. Moreover, we study invariant spin divisors under automorphisms and antiholomorphic involutions of Riemann surfaces and count them. We generalize a formula that gives 2-spin divisors, proved by Mumford, to the case of m-spin divisors for an even m, supported on branch points of a hyperelliptic surface.