Asymptotically cylindrical Calabi–Yau 3–folds from weak Fano 3–folds

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Title: Asymptotically cylindrical Calabi–Yau 3–folds from weak Fano 3–folds
Authors: Corti, A
Haskins, M
Nordström, J
Pacini, T
Item Type: Journal Article
Abstract: We prove the existence of asymptotically cylindrical (ACyl) Calabi–Yau 3–folds starting with (almost) any deformation family of smooth weak Fano 3–folds. This allow us to exhibit hundreds of thousands of new ACyl Calabi–Yau 3–folds; previously only a few hundred ACyl Calabi–Yau 3–folds were known. We pay particular attention to a subclass of weak Fano 3–folds that we call semi-Fano 3–folds. SemiFano 3–folds satisfy stronger cohomology vanishing theorems and enjoy certain topological properties not satisfied by general weak Fano 3–folds, but are far more numerous than genuine Fano 3–folds. Also, unlike Fanos they often contain P 1 s with normal bundle O.1/ ˚ O.1/, giving rise to compact rigid holomorphic curves in the associated ACyl Calabi–Yau 3–folds. We introduce some general methods to compute the basic topological invariants of ACyl Calabi–Yau 3–folds constructed from semi-Fano 3–folds, and study a small number of representative examples in detail. Similar methods allow the computation of the topology in many other examples. All the features of the ACyl Calabi–Yau 3–folds studied here find application in [17] where we construct many new compact G2 –manifolds using Kovalev’s twisted connected sum construction. ACyl Calabi–Yau 3–folds constructed from semi-Fano 3–folds are particularly well-adapted for this purpose.
Issue Date: 15-Jul-2013
Date of Acceptance: 4-Mar-2013
URI: http://hdl.handle.net/10044/1/43225
DOI: https://dx.doi.org/10.2140/gt.2013.17.1955
ISSN: 1465-3060
Start Page: 1955
End Page: 2059
Journal / Book Title: Geometry & Topology
Volume: 17
Issue: 4
Copyright Statement: © 2013 Mathematical Sciences Publishers.
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: EP/G007241/1
EP/G06170X/1
EP/L001527/1
Keywords: Science & Technology
Physical Sciences
Mathematics
MATHEMATICS
CANONICAL SINGULARITIES
BIRATIONAL MAPS
RICCI CURVATURE
MINIMAL MODELS
GENERAL TYPE
BLOWING-UP
THREEFOLDS
POINTS
NUMBER
VARIETIES
math.AG
math.DG
14J30, 53C29 (Primary) 14E15, 14J28, 14J32, 14J45, 53C25 (Secondary)
Geological & Geomatics Engineering
0101 Pure Mathematics
Publication Status: Published
Appears in Collections:Pure Mathematics
Mathematics
Faculty of Natural Sciences



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