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Article: Desingularizations of Calabi-Yau 3-folds with conical singularities. II. The obstructed case.

TitleDesingularizations of Calabi-Yau 3-folds with conical singularities. II. The obstructed case.
Authors
Issue Date2009
PublisherOxford University Press. The Journal's web site is located at http://qjmath.oxfordjournals.org/
Citation
The Quarterly Journal of Mathematics , 2009, v. 60 n. 1, p. 1-44 How to Cite?
AbstractThis is the second of two papers studying Calabi–Yau 3-folds with conical singularities and their desingularizations. In our first paper [Y.-M. Chan, Quart. J. Math. 57 (2006), 151–181] we constructed the desingularization of the conically singular manifold M0 by gluing an asymptotically conical (AC) Calabi–Yau 3-fold Y into M0 at the singular point, thus obtaining a 1-parameter family of compact, non-singular Calabi–Yau 3-folds Mt for small t > 0. During the gluing process one may encounter a kind of cohomological obstruction to defining a 3-form Ωt on Mt which interpolates between the 3-form Ω0 on M0 and the scaled 3-form t3 ΩY on Y if the rate λ at which the AC Calabi–Yau 3-fold Y converges to the Calabi–Yau cone is equal to − 3. The first paper [3] studied the simpler case λ < −3 where there is no obstruction. This paper extends the result in the first one by considering a more complicated situtation when λ = −3. Assuming the existence of singular Calabi–Yau metrics on compact complex 3-folds with ordinary double points, our result in this paper can be applied to repairing such kinds of singularities, which is an analytic version of Friedman's result giving necessary and sufficient conditions for smoothing ordinary double points.
Persistent Identifierhttp://hdl.handle.net/10722/197205
ISSN
2015 Impact Factor: 0.853
2015 SCImago Journal Rankings: 1.289
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorChan, YMen_US
dc.date.accessioned2014-05-23T02:26:44Z-
dc.date.available2014-05-23T02:26:44Z-
dc.date.issued2009en_US
dc.identifier.citationThe Quarterly Journal of Mathematics , 2009, v. 60 n. 1, p. 1-44en_US
dc.identifier.issn0033-5606-
dc.identifier.urihttp://hdl.handle.net/10722/197205-
dc.description.abstractThis is the second of two papers studying Calabi–Yau 3-folds with conical singularities and their desingularizations. In our first paper [Y.-M. Chan, Quart. J. Math. 57 (2006), 151–181] we constructed the desingularization of the conically singular manifold M0 by gluing an asymptotically conical (AC) Calabi–Yau 3-fold Y into M0 at the singular point, thus obtaining a 1-parameter family of compact, non-singular Calabi–Yau 3-folds Mt for small t > 0. During the gluing process one may encounter a kind of cohomological obstruction to defining a 3-form Ωt on Mt which interpolates between the 3-form Ω0 on M0 and the scaled 3-form t3 ΩY on Y if the rate λ at which the AC Calabi–Yau 3-fold Y converges to the Calabi–Yau cone is equal to − 3. The first paper [3] studied the simpler case λ < −3 where there is no obstruction. This paper extends the result in the first one by considering a more complicated situtation when λ = −3. Assuming the existence of singular Calabi–Yau metrics on compact complex 3-folds with ordinary double points, our result in this paper can be applied to repairing such kinds of singularities, which is an analytic version of Friedman's result giving necessary and sufficient conditions for smoothing ordinary double points.-
dc.languageengen_US
dc.publisherOxford University Press. The Journal's web site is located at http://qjmath.oxfordjournals.org/-
dc.relation.ispartofThe Quarterly Journal of Mathematicsen_US
dc.titleDesingularizations of Calabi-Yau 3-folds with conical singularities. II. The obstructed case.en_US
dc.typeArticleen_US
dc.identifier.emailChan, YM: wtymchan@hku.hken_US
dc.description.naturelink_to_OA_fulltext-
dc.identifier.doi10.1093/qmath/ham049-
dc.identifier.hkuros162814en_US
dc.identifier.volume60en_US
dc.identifier.issue1-
dc.identifier.spage1en_US
dc.identifier.epage44en_US
dc.identifier.isiWOS:000263606300001-
dc.publisher.placeUnited Kingdom-

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