### Abstract

In this chapter we outline some applications of Homological Mirror Symmetry to classical problems in Algebraic Geometry, like rationality of algebraic varieties and the study of algebraic cycles. Several examples are studied in detail.

Original language | English (US) |
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Title of host publication | Homological Mirror Symmetry |

Subtitle of host publication | New Developments and Perspectives |

Editors | Anton Kapustin, Maximilian Kreuzer, Karl-Georg Schlesinger |

Pages | 125-152 |

Number of pages | 28 |

DOIs | |

State | Published - Jan 7 2009 |

### Publication series

Name | Lecture Notes in Physics |
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Volume | 757 |

ISSN (Print) | 0075-8450 |

### ASJC Scopus subject areas

- Physics and Astronomy (miscellaneous)

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## Cite this

Katzarkov, L. (2009). Homological mirror symmetry and algebraic cycles. In A. Kapustin, M. Kreuzer, & K-G. Schlesinger (Eds.),

*Homological Mirror Symmetry: New Developments and Perspectives*(pp. 125-152). (Lecture Notes in Physics; Vol. 757). https://doi.org/10.1007/978-3-540-68030-7_5