Hodge theoretic aspects of mirror symmetry

@article{Katzarkov2008HodgeTA,
title={Hodge theoretic aspects of mirror symmetry},
author={Ludmil Katzarkov and Maxim Kontsevich and Tony Pantev},
journal={arXiv: Algebraic Geometry},
year={2008}
}
• Published 31 May 2008
• Mathematics
• arXiv: Algebraic Geometry
We discuss the Hodge theory of algebraic non-commutative spaces and analyze how this theory interacts with the Calabi-Yau condition and with mirror symmetry. We develop an abstract theory of non-commutative Hodge structures, investigate existence and variations, and propose explicit construction and classification techniques. We study the main examples of non-commutative Hodge structures coming from a symplectic or a complex geometry possibly twisted by a potential. We study the interactions of…
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