Tropical and Algebraic Curves with Multiple Points

Abstract

Patchworking theorems serve as a basic element of the correspondence between tropical and algebraic curves, which is a core area of tropical enumerative geometry. We present a new version of a patchworking theorem that relates plane tropical curves to complex and real algebraic curves having prescribed multiple points. It can be used to compute Welschinger invariants of nontoxic del Pezzo surfaces.