On large configurations of lines on quartic surfaces

Abstract

We estimate the number of lines on a non-K3 quartic surface. Such a surface with only isolated double point(s) contains at most twenty lines; this bound is attained by a unique configuration of lines and by a surface with a certain limited set of singularities. We have similar itemized bounds for other types of non-simple singularities, which culminate in at most 31 lines on a non-K3 quartic not ruled by lines; this bound is only attained on the quartic monoids described by K.~Rohn.