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arXiv · 2309.02154

Mirror symmetric Gamma conjecture for del Pezzo surfaces

Bohan Fang·Junxiao Wang·Yan Zhou
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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.

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Bohan Fang, Junxiao Wang, Yan Zhou. 2023-09-05. Mirror symmetric Gamma conjecture for del Pezzo surfaces. https://arxiv.org/abs/2309.02154

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