Enumerative invariants from cuspidal curves.

Enumerative geometry deals with the study of counting problems in geometric spaces. Example questions are:
“How many conics are there through 5 points in the plane?”
“How many lines are there on a cubic surface?”
“How many curves are there on a quintic threefold?”
A powerful tool to study enumerative problems is given by Gromov—Witten invariants. These are supposed to give answers to enumerative problems, but in this talk, I will show that this expectation is wrong. I will instead introduce “reduced” invariants from cuspidal curves, which are more enumerative, and I will discuss a relation between standard and reduced Gromov—Witten invariants.