Deformations of compact complex surfaces II

Lagrangian Floer Theory on Compact Toric Manifolds Ii : Bulk Deformations

This is a continuation of part I in the series (in progress) of the papers on Lagrangian Floer theory on toric manifolds. Using the deformations of Floer cohomology by the ambient cycles, which we call bulk deformations, we find a continuum of non-displaceable Lagrangian fibers on some compact toric manifolds. We also provide a method of finding all those fibers in arbitrary compact toric manif...

Nonuniformisable Foliations on Compact Complex Surfaces

We give a complete classification of holomorphic foliations on compact complex surfaces which are not uniformisable, i.e., for which universal coverings of the leaves do not glue together in a Hausdorff way. This leads to complex analogs of the Reeb component defined on certain Hopf surfaces and certain Kato surfaces. 2000 Math. Subj. Class. 32J15, 37F75, 57R30.

A Crash Course on Compact Complex Surfaces

“Analytic invariants” of complex manifolds that the generalizations of the genus of curves, and their birationally invariant nature. Blow-up of a surface at a point. Birational classification of complex surfaces via minimal models. Enriques-Kodaira classification. Canonical models. Calabi-Yau manifolds and K3 surfaces. Fano manifolds and del Pezzo surfaces. A Crash Course onCompact Complex Surf...

Compact Deformations of Fuchsian Groups

A Willmore functional for compact surfaces of complex projective plane

where H denotes the mean curvature vector of the immersion φ, K̄ the sectional curvature of M restricted to Σ and dA the canonical measure of the induced metric. This functional has been extensively studied when M is the Euclidean space R (or the sphere S or the hyperbolic space RH, because W is invariant under conformal transformations of ambient space). The type of problems which have been stu...