# Large Complex Structure Limits of K3 Surfaces

@article{Gross2000LargeCS, title={Large Complex Structure Limits of K3 Surfaces}, author={Mark Gross and Pelham M. H. Wilson}, journal={Journal of Differential Geometry}, year={2000}, volume={55}, pages={475-546} }

Motivated by the picture of mirror symmetry suggested by Strominger, Yau and Zaslow, we made a conjecture concerning the Gromov-Hausdorff limits of Calabi-Yau n-folds (with Ricci-flat K\"ahler metric) as one approaches a large complex structure limit point in moduli; a similar conjecture was made independently by Kontsevich, Soibelman and Todorov. Roughly stated, the conjecture says that, if the metrics are normalized to have constant diameter, then this limit is the base of the conjectural… Expand

#### 259 Citations

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In this paper we discuss two major conjectures in Mirror Symmetry: Strominger-Yau-Zaslow conjecture about torus fibrations, and the homological mirror conjecture (about an equivalence of the Fukaya… Expand

Limits of Calabi–Yau metrics when the Kähler class degenerates

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We study the behavior of families of Ricci-flat Kahler metrics on a projective Calabi- Yau manifold when the Kahler classes degenerate to the boundary of the ample cone. We prove that if the limit… Expand

Collapsing of abelian fibred Calabi-Yau manifolds

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- 2011

We study the collapsing behaviour of Ricci-flat Kahler metrics on a projective Calabi-Yau manifold which admits an abelian fibration, when the volume of the fibers approaches zero. We show that away… Expand

Geometric Aspects of Mirror Symmetry (with SYZ for Rigid CY manifolds)

- Physics, Mathematics
- 2002

In this article we discuss the geometry of moduli spaces of (1) flat bundles over special Lagrangian submanifolds and (2) deformed Hermitian-Yang-Mills bundles over complex submanifolds in Calabi-Yau… Expand

Conifold transitions via affine geometry and mirror symmetry

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- 2013

Mirror symmetry of Calabi-Yau manifolds can be understood via a Legendre duality between a pair of certain affine manifolds with singularities called tropical manifolds. In this article, we study… Expand

Affine manifolds, log structures, and mirror symmetry

- Mathematics
- 2002

This is an outline of work in progress concerning an algebro-geometric form of the Strominger-Yau-Zaslow conjecture. We introduce a limited type of degeneration of Calabi-Yau manifolds, which we call… Expand

Affine manifolds, SYZ geometry, and the 'Y' vertex

- Mathematics, Physics
- 2004

We study the real Monge-Ampere equation in two and three dimensions, both from the point of view of the SYZ conjecture, where solutions give rise to semi-flat Calabi-Yau’s and in affine differential… Expand

Homological mirror symmetry for hypertoric varieties I : conic equivariant sheaves

- 2018

We consider homological mirror symmetry in the context of hypertoric varieties, showing that an appropriate category of B-branes (that is, coherent sheaves) on an additive hypertoric variety matches… Expand

Remarks on degenerations of hyper-K\"ahler manifolds

- Mathematics
- 2017

Using the Minimal Model Program, any degeneration of K-trivial varieties can be arranged to be in a Kulikov type form, i.e. with trivial relative canonical divisor and mild singularities. In the… Expand

K3 surfaces from configurations of six lines in ℙ2 and mirror symmetry II—λK3-functions

- Mathematics
- 2018

From the viewpoint of mirror symmetry, we revisit the hypergeometric system $E(3,6)$ for a family of K3 surfaces. We construct a good resolution of the Baily-Borel-Satake compactification of its… Expand

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