Relative Clifford inequality for varieties fibered by curves

Abstract

We prove a sharp relative Clifford inequality for relatively special divisors on varieties fibered by curves. It generalizes the classical Clifford inequality about a single curve to a fibration of curves. It yields a geographical inequality for varieties Albanese-fibered by curves. We also apply it to deduce a slope inequality for some higher dimensional families of curves. It sheds light on the existence of a more general Cornalba–Harris–Xiao type inequality for families of curves.