Quantum Cohomology and Crepant Resolutions: A Conjecture

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dc.creatorCoates, Tom
dc.creatorRuan, Yongbin
dc.date2007-10-31
dc.date2008-04-16
dc.date.accessioned2026-07-07T09:32:35Z
dc.date.available2026-07-07T09:32:35Z
dc.descriptionWe give an expository account of a conjecture, developed by Coates--Corti--Iritani--Tseng and Ruan, which relates the quantum cohomology of a Gorenstein orbifold X to the quantum cohomology of a crepant resolution Y of X. We explore some consequences of this conjecture, showing that it implies versions of both the Cohomological Crepant Resolution Conjecture and of the Crepant Resolution Conjectures of Ruan and Bryan--Graber. We also give a "quantized" version of the conjecture, which determines higher-genus Gromov--Witten invariants of X from those of Y.
dc.description34 pages. Version 2: added a paragraph (Remark 4.2) clarifying the history and origins of the conjecture. Version 3: corrected some typos in Section 8
dc.identifierhttps://arxiv.org/abs/0710.5901
dc.identifierhttp://arxiv.org/abs/0710.5901
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/158830
dc.subjectAlgebraic Geometry
dc.subjectMathematical Physics
dc.subject14N35 (Primary); 14A20, 83E30 (Secondary)
dc.titleQuantum Cohomology and Crepant Resolutions: A Conjecture
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