Homological mirror symmetry for the quintic 3–fold

Nohara, Yuichi; Ueda, Kazushi

doi:10.2140/gt.2012.16.1967

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Homological mirror symmetry for the quintic 3–fold

Yuichi Nohara and Kazushi Ueda

Geometry & Topology 16 (2012) 1967–2001

DOI: 10.2140/gt.2012.16.1967

Abstract

We prove homological mirror symmetry for the quintic Calabi–Yau 3–fold. The proof follows that for the quartic surface by Seidel closely, and uses a result of Sheridan. In contrast to Sheridan’s approach, our proof gives the compatibility of homological mirror symmetry for the projective space and its Calabi–Yau hypersurface.

Keywords

homological mirror symmetry

Mathematical Subject Classification 2010

Primary: 53D37

Secondary: 14J33

References

Publication

Received: 21 September 2011

Revised: 9 May 2012

Accepted: 21 June 2012

Published: 27 August 2012

Proposed: Jim Bryan

Seconded: Richard Thomas, Simon Donaldson

Authors

Yuichi Nohara
Faculty of Education Kagawa University 1-1 Saiwai-cho Takamatsu 760-8522 Japan

Kazushi Ueda
Department of Mathematics Osaka University Graduate School of Science Machikaneyama 1-1 Toyonaka 560-0043 Japan
http://www.math.sci.osaka-u.ac.jp/~kazushi/

Volume 16, issue 4 (2012)