Hodge theoretic aspects of mirror symmetry

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dc.creatorKatzarkov, L.
dc.creatorKontsevich, M.
dc.creatorPantev, T.
dc.date2008-05-31
dc.date.accessioned2026-07-07T09:42:06Z
dc.date.available2026-07-07T09:42:06Z
dc.descriptionWe 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 the new Hodge theoretic invariants with mirror symmetry and derive non-commutative analogues of some of the more interesting consequences of Hodge theory such as unobstructedness and the construction of canonical coordinates on moduli.
dc.description124 pages, 8 figures
dc.identifierhttps://arxiv.org/abs/0806.0107
dc.identifierhttp://arxiv.org/abs/0806.0107
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/162063
dc.subjectAlgebraic Geometry
dc.subjectHigh Energy Physics - Theory
dc.subjectSymplectic Geometry
dc.subject14C30, 14J32, 19D55, 34M40
dc.titleHodge theoretic aspects of mirror symmetry
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