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Asymptotically cylindrical Calabi–Yau 3–folds from weak Fano 3–folds
File | Description | Size | Format | |
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1206.2277v3.pdf | Accepted version | 980.81 kB | Adobe PDF | View/Open |
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 Faculty of Natural Sciences Mathematics |