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Katzarkov has proposed a generalization of Kontsevich's mirror symmetryconjecture, covering some varieties of general type. Seidel \cite{Se} hasproved a version of this conjecture in the simplest case of the genus twocurve. Basing on the paper of Seidel, we prove the conjecture (in the sameversion) for curves of genus $g\geq 3,$ relating the Fukaya category of a genus$g$ curve to the category of Landau-Ginzburg branes on a certain singularsurface. We also prove a kind of reconstruction theorem for hypersurfacesingularities. Namely, formal type of hypersurface singularity (i.e. a formalpower series up to a formal change of variables) can be reconstructed, withsome technical assumptions, from its D$(\Z/2)$-G category of Landau-Ginzburgbranes. The precise statement is Theorem 1.2.

Homological mirror symmetry for curves of higher genus