Misha Verbitsky
Locally conformally Kähler manifolds
Brief description of the course
Slides
Lecture 1:
LCK manifolds: introduction and definitions.
Lecture 2:
Vaisman theorem.
Lecture 3:
Vaisman manifolds (local geometry).
Lecture 4:
Sasakian manifolds.
Lecture 5:
Structure theorem for Vaisman manifolds.
Lecture 6:
Orbifolds.
Lecture 7:
Immersion theorem for Vaisman manifolds.
Lecture 8:
LCK manifolds with potential.
Lecture 9:
Holomorphic contractions.
Lecture 10:
CR-geometry and pseudoconvex shells.
Lecture 11:
CR-geometry of Sasakian manifolds
Lecture 12:
Morse-Novikov cohomology.
Lecture 13:
Automorphisms of LCK manifolds.
Lecture 14:
Oeljeklaus-Toma manifolds.
Lecture 15:
Classification of complex surfaces.
Handouts
Handout 1:
local systems and Morse-Novikov cohomology (February 10).
Handout 2:
Hermitian manifolds (February 17).
Handout 3:
homotheties on Riemannian manifolds (February 23).
Handout 4:
Sasakian manifolds (March 03).
Handout 5:
Groups of automorphisms (March 10).
Handout 6:
Orbifolds (March 17).
Handout 7:
Hopf manifolds (March 31).
Handout 8:
Normal families (April 07).
Handout 10:
Levi form (April 21).
Handout 11:
CR vs. Sasakian (April 28).
Handout 12:
Morse-Novikov and Bott-Chern cohomology (May 12).
Handout 13:
Conformal symplectomorphisms (May 26).
Laboratory of Algebraic Geometry and its Applications