The flex divisor of a K3 surface

Abstract

The flex divisor R flex of a primitively polarized K3 surface (X, L) is, generically, the set of all points x ∈ X for which there exists a pencil V ⊂ |L| whose base locus is {x}. We show that ifwhere C(d) is the Catalan number. We also show that there is a well-defined notion of flex divisor over the whole moduli space F 2d of polarized K3 surfaces.