NONHYPERELLIPTIC FIBRATIONS OF GENUS 4 WITH NONSURJECTIVE MULTIPLICATION MAP

Abstract

AbstractWe prove some numerical inequality for the Horikawa indices for Eisenbud–Harris special nonhyperelliptic fibrations of genus 4 on algebraic surfaces under the assumption that the multiplication map of the fibration is not surjective. Furthermore, we prove that the inequality is best possible by constructing the examples satisfying the equality.