Gromov--Witten invariants with naive tangency conditions

Author:

Felix Janda, Tony Yue Yu

Keyword:

Mathematics, Algebraic Geometry, Algebraic Geometry (math.AG), Symplectic Geometry (math.SG)

journal:

date:

2023-10-18 16:00:00

Abstract

We introduce Gromov-Witten invariants with naive tangency conditions at the marked points of the source curve. We then establish an explicit formula which expresses Gromov-Witten invariants with naive tangency conditions in terms of descendent Gromov-Witten invariants. Several examples of genus zero Gromov-Witten invariants with naive tangencies are computed in the case of curves and surfaces. In particular, the counts of rational curves naively tangent to an anticanonical divisor on a del Pezzo surface are studied, and via mirror symmetry, we obtain a relation to the local Gromov-Witten invariants.

PDF: Gromov--Witten invariants with naive tangency conditions.pdf