Quasi-asymptotically conical Calabi-Yau manifolds

@article{Conlon2016QuasiasymptoticallyCC,
  title={Quasi-asymptotically conical Calabi-Yau manifolds},
  author={Ronan J. Conlon and A. Degeratu and Fr'ed'eric Rochon},
  journal={arXiv: Differential Geometry},
  year={2016}
}
We construct new examples of quasi-asymptotically conical (QAC) Calabi-Yau manifolds that are not quasi-asymptotically locally Euclidean (QALE). We do so by first providing a natural compactification of QAC-spaces by manifolds with fibred corners and by giving a definition of QAC-metrics in terms of an associated Lie algebra of smooth vector fields on this compactification. Thanks to this compactification and the Fredholm theory for elliptic operators on QAC-spaces developed by the second… Expand

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References

SHOWING 1-10 OF 40 REFERENCES
The Moduli Space of Asymptotically Cylindrical Calabi–Yau Manifolds
We prove that the deformation theory of compactifiable asymptotically cylindrical Calabi–Yau manifolds is unobstructed. This relies on a detailed study of the Dolbeault–Hodge theory and itsExpand
Asymptotically conical Calabi-Yau manifolds, III
This is the first part in a two-part series on complete Calabi-Yau manifolds asymptotic to Riemannian cones at infinity. We begin by proving general existence and uniqueness results. The uniquenessExpand
Examples of asymptotically conical Ricci-flat Kähler manifolds
Previously the author has proved that a crepant resolution π : Y → X of a Ricci-flat Kähler cone X admits a complete Ricci-flat Kähler metric asymptotic to the cone metric in every Kähler class inExpand
Compact Moduli Spaces of Del Pezzo Surfaces and K\"ahler-Einstein metrics
We prove that the Gromov-Hausdorff compactification of the moduli space of Kahler-Einstein Del Pezzo surfaces in each degree agrees with certain algebro-geometric compactification. In particular,Expand
FANO MANIFOLDS, CONTACT STRUCTURES, AND QUATERNIONIC GEOMETRY
Let Z be a compact complex (2n+1)-manifold which carries a complex contact structure, meaning a codimension-1 holomorphic sub-bundle D⊂TZ which is maximally non-integrable. If Z admits aExpand
On The Ricci Curvature of a Compact Kahler Manifold and the Complex Monge-Ampere Equation, I*
Therefore a necessary condition for a (1,l) form ( G I a ' r r ) I,,, Rlr dz' A d? to be the Ricci form of some Kahler metric is that it must be closed and its cohomology class must represent theExpand
Quasi-ALE Metrics with Holonomy SU(m) and Sp(m)
Let G be a finite subgroup of U(m),and X a resolution of ℂm/G. We define aspecial class of Kähler metrics g on Xcalled Quasi Asymptotically Locally Euclidean (QALE) metrics. Thesesatisfy aExpand
Asymptotically Locally Euclidean Metrics with Holonomy SU(m)
Let G be a finite subgroup of U(m) such thatℂm/G has an isolated singularity at 0. Let X be a resolution of ℂm/G, andg a Kähler metric on X. We callg Asymptotically Locally Euclidean (ALE) if itExpand
Hodge cohomology of some foliated boundary and foliated cusp metrics
For fibred boundary and fibred cusp metrics, Hausel, Hunsicker, and Mazzeo identified the space of $L^2$ harmonic forms of fixed degree with the images of maps between intersection cohomology groupsExpand
Compact Manifolds with Special Holonomy
The book starts with a thorough introduction to connections and holonomy groups, and to Riemannian, complex and Kahler geometry. Then the Calabi conjecture is proved and used to deduce the existenceExpand
...
1
2
3
4
...