Refined broccoli invariants
Lothar Göttsche, Franziska Schroeter · Journal of Algebraic Geometry · 2018
We introduce a tropical enumerative invariant depending on a variable y y which generalizes the tropical refined Severi degree. We show that this refined broccoli invariant is indeed independent of the point configuration, and that it specializes to a tropical descendant Gromov-Witten invariant for y = 1 y=1 and to the corresponding broccoli invariant for y = − 1 y=-1 . Furthermore, we define tropical refined descendant Gromov-Witten invariants which equal the corresponding refined broccoli invariants giving a new insight to the nature of broccoli invariants. We discuss various possible generalizations e.g. to refinements of bridge curves and Welschinger curves.