Certain holomorphic sections relating to 2-pointed Weierstrass gap sets on a compact Riemann surface

Abstract

For a compact Riemann surface X of genus g, we will construct a holomorphic section of the line bundle π₁^*K_X^{g(g+1)(g+2)/6} $\otimes$ π₂^*K_X^{g(g+1)(g+2)/6} over X × X whose zero set consists exactly of the points (P,Q) with the cardinalities of the Weierstrass gap sets G(P,Q) greater than the minimal value (g² + 3g)/2.