Imperial College London
Alternate

ProfessorAlessioCorti

Faculty of Natural Sciences, Department of Mathematics

Chair in Pure Mathematics
 
 
 
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Contact

 

+44 (0)20 7594 1870a.corti Website

 
 
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Location

 

673Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Corti:2013:10.2140/gt.2013.17.1955,
author = {Corti, A and Haskins, M and Nordström, J and Pacini, T},
doi = {10.2140/gt.2013.17.1955},
journal = {Geometry & Topology},
pages = {1955--2059},
title = {Asymptotically cylindrical Calabi–Yau 3–folds from weak Fano 3–folds},
url = {http://dx.doi.org/10.2140/gt.2013.17.1955},
volume = {17},
year = {2013}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - We prove the existence of asymptotically cylindrical (ACyl) Calabi–Yau 3–foldsstarting with (almost) any deformation family of smooth weak Fano 3–folds. Thisallow us to exhibit hundreds of thousands of new ACyl Calabi–Yau 3–folds; previouslyonly a few hundred ACyl Calabi–Yau 3–folds were known. We pay particularattention to a subclass of weak Fano 3–folds that we call semi-Fano 3–folds. SemiFano3–folds satisfy stronger cohomology vanishing theorems and enjoy certaintopological properties not satisfied by general weak Fano 3–folds, but are far morenumerous than genuine Fano 3–folds. Also, unlike Fanos they often contain P1s withnormal bundle O.1/ O.1/,giving rise to compact rigid holomorphic curves inthe associated ACyl Calabi–Yau 3–folds.We introduce some general methods to compute the basic topological invariants ofACyl Calabi–Yau 3–folds constructed from semi-Fano 3–folds, and study a smallnumber of representative examples in detail. Similar methods allow the computationof 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 twistedconnected sum construction. ACyl Calabi–Yau 3–folds constructed from semi-Fano3–folds are particularly well-adapted for this purpose.
AU  - Corti,A
AU  - Haskins,M
AU  - Nordström,J
AU  - Pacini,T
DO  - 10.2140/gt.2013.17.1955
EP  - 2059
PY  - 2013///
SN  - 1465-3060
SP  - 1955
TI  - Asymptotically cylindrical Calabi–Yau 3–folds from weak Fano 3–folds
T2  - Geometry & Topology
UR  - http://dx.doi.org/10.2140/gt.2013.17.1955
UR  - http://hdl.handle.net/10044/1/43225
VL  - 17
ER  -
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