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The Gepner-like models of $k^{K}$-type is considered. When $k+2$ is multipleof $K$ the elliptic genus and the Euler characteristic is calculated. Usingfree-field representation we relate these models with $\sigma$-models onhypersurfaces in the total space of anticanonical bundle over the projectivespace $\mathbb{P}^{K-1}$.

Gepner-like models and Landau-Ginzburg/sigma-model correspondence