Weierstrass Gap Sets for Quadruples of Points on Compact Riemann Surfaces

Abstract

Let M be a compact Riemann surface of genus g , and let P 1 ,…, P 4 be distinct points on M . We study the Weierstrass gap set G ( P 1 ,…, P 4 ) and prove the conjecture of Ballico and Kim on the upper bound of # G ( P 1 ,…, P 4 ) affirmatively in case M is d -gonal curve of genus g ≥ 5 with d = 2 or d ≥ 5.