Mirror symmetric Gamma conjecture for del Pezzo surfaces

Author:

Bohan Fang, Junxiao Wang, Yan Zhou

Keyword:

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

journal:

date:

2023-09-04 16:00:00

Abstract

For a del Pezzo surface of degree $\geq 3$, we compute the oscillatory integral for its mirror Landau-Ginzburg model in the sense of Gross-Hacking-Keel [Mark Gross, Paul Hacking, and Sean Keel, "Mirror symmetry for log Calabi-Yau surfaces I". In: Publ. Math. Inst. Hautes Etudes Sci. 122 (2015), pp. 65-168]. We explicitly construct the mirror cycle of a line bundle and show that the leading order of the integral on this cycle involves the twisted Chern character and the Gamma class. This proves a version of the Gamma conjecture for non-toric Fano surfaces with an arbitrary K-group insertion.

PDF: Mirror symmetric Gamma conjecture for del Pezzo surfaces.pdf