Show simple item record

dc.contributor.authorLin, Yu-Shenen_US
dc.contributor.authorCollins, Tristanen_US
dc.contributor.authorJacob, Adamen_US
dc.date.accessioned2020-04-28T13:31:45Z
dc.date.available2020-04-28T13:31:45Z
dc.date.issued2020-04-17
dc.identifierhttps://arxiv.org/abs/1904.08363
dc.identifier.citationYu-Shen Lin, Tristan Collins, Adam Jacob. 2020. "Special Lagrangian submanifolds of log Calabi-Yau manifolds." preprint, arXiv: 1904.08363, https://arxiv.org/abs/1904.08363
dc.identifier.urihttps://hdl.handle.net/2144/40387
dc.description.abstractWe study the existence of special Lagrangian submanifolds of log Calabi-Yau manifolds equipped with the complete Ricci-flat Kähler metric constructed by Tian-Yau. We prove that if X is a Tian-Yau manifold, and if the compact Calabi-Yau manifold at infinty admits a single special Lagrangian, then X admits infinitely many disjoint special Lagrangians. In complex dimension 2, we prove that if Y is a del Pezzo surface, or a rational elliptic surface, and D∈|−KY| is a smooth divisor with D2=d, then X=Y∖D admits a special Lagrangian torus fibration, as conjectured by Strominger-Yau-Zaslow and Auroux. In fact, we show that X admits twin special Lagrangian fibrations, confirming a prediction of Leung-Yau. In the special case that Y is a rational elliptic surface, or Y=ℙ2 we identify the singular fibers for generic data, thereby confirming two conjectures of Auroux. Finally, we prove that after a hyper-Kähler rotation, X can be compactified to the complement of a Kodaira type Id fiber appearing as a singular fiber in a rational elliptic surface πˇ:Yˇ→ℙ1.en_US
dc.description.urihttps://arxiv.org/abs/1904.08363
dc.language.isoen_US
dc.relation.ispartofpreprint, arXiv: 1904.08363
dc.subjectMathematicsen_US
dc.subjectDifferential geometryen_US
dc.subjectSymplectic geometryen_US
dc.titleSpecial Lagrangian submanifolds of log Calabi-Yau manifoldsen_US
dc.typeArticleen_US
pubs.elements-sourcemanual-entryen_US
pubs.notesEmbargo: No embargoen_US
pubs.organisational-groupBoston Universityen_US
pubs.organisational-groupBoston University, College of Arts & Sciencesen_US
pubs.organisational-groupBoston University, College of Arts & Sciences, Department of Mathematics & Statisticsen_US
pubs.publication-statusSubmitteden_US
dc.description.oaversionFirst author draft
dc.identifier.mycv519206


This item appears in the following Collection(s)

Show simple item record