On Landau-Ginzburg models for Fano varieties. (English) Zbl 1194.14065

Przyjalkowski, Victor

Commun. Number Theory Phys. 1, No. 4, 713-728 (2008).

Mirror symmetry was originally formulated for Calabi-Yau manifolds and was later generalized to Fano varieties. A mirror to a Fano variety \(X\) is a Landau-Ginzburg model, a non-compact complex manifold \(M\) with a complex-valued function \(f\) on it, called the superpotential. The paper under review discusses a general strategy for finding mirrors to Fano threefolds, providing explicit answers for threefolds with Picard group \(\mathbb{Z}\) of genera \(9\), \(10\) and \(12\).

Reviewer: Ivan Cheltsov (Edinburgh)

MSC:

14J45

Fano varieties

Keywords:

mirror symmetry; Fano varieties