FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2001, VOLUME 7, NUMBER 2, PAGES 423-431

A. V. Krotov

V. V. Rabotin

Abstract

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We consider the family of smooth
```$n$ -dimensional toric
manifolds generalizing the family of Hirzebruch
surfaces to dimension $n$ . We analyze conditions
under which there exists a Calabi--Yau complete intersection of
two ample hypersurfaces in these manifolds. This turns out to
be possible only if the toric manifold is the product of projective spaces. If one of
the hypersurfaces is not ample then we find Calabi--Yau complete
intersection of two hypersurfaces in Fano manifolds of the given family.

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Last modified: October 31, 2001.