The Physical Mirror Equivalence for the Local P^2
Sergio Luigi Cacciatori, Marco Compagnoni, Stefano Guerra
TL;DR
This paper establishes a precise physical mirror equivalence between the derived category of the canonical bundle of P^2 and the Fukaya category of its mirror, integrating mirror symmetry, moduli spaces, and Gromov-Witten invariants.
Contribution
It provides a rigorous proof of the mirror equivalence for the total space of the canonical bundle of P^2, confirming compatibility with mirror maps and Gromov-Witten invariants.
Findings
Confirmed the mirror equivalence between D^b(K_{P^2}) and Fukaya category.
Demonstrated compatibility with mirror maps and moduli space structures.
Validated the correspondence through Gromov-Witten invariants computations.
Abstract
In this paper we consider the total space of the canonical bundle of P^2 and we use a proposal by Hosono, together with results in Seidel and Auroux-Katzarkov-Orlov, to deduce the right physical mirror equivalence between D^b(K_{P^2}) and the derived Fukaya category of its mirror. By construction, our equivalence is compatible with the mirror map between moduli spaces and with the computation of Gromov--Witten invariants.
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