Misha Verbitsky

Instituto Nacional de Matemática Pura e Aplicada

Complex Surfaces

Slides:

• Lecture 1: Kodaira-Enriques classification for non-algebraic surfaces, 06.01.2025
• Lecture 2: Hopf manifolds and Vaisman manifolds, 08.01.2025
• Lecture 3: Chern connection, 10.01.2025
• Lecture 4: Locally conformally Kähler manifolds: definition and examples, 13.01.2025
• Lecture 5: Locally conformally Kähler manifolds in terms of local systems, 15.01.2025
• Lecture 6: Vaisman theorem, 17.01.2025
• Lecture 7: Elliptic operators of second order, 22.01.2025
• Lecture 7 bis: Elliptic operators, a supplementary lecture (for home reading).
• Lecture 8: Adjoint operators, 24.01.2025
• Lecture 9: The index theorem, 27.01.2025
• Lecture 10: Gauduchon metrics, 29.01.2025
• Lecture 11: Bott-Chern cohomology and defect of a complex surface, 31.01.2025
• Lecture 12: First cohomology of a complex surface, 03.02.2025
• Lecture 13: Currents, 05.02.2025
• Lecture 14: Pseudo-effective cone, Gauduchon cone and Hahn-Banach theorem, 08.02.2025
• Lecture 15: Plurisubharmonic and subharmonic functions, 10.02.2025
• Lecture 16: Integral transform, 12.02.2025
• Lecture 17: Poincaré-Lelong formula, 14.02.2025
• Lecture 18: Surfaces of Fujiki class C, 17.02.2025
• Lecture 19: Bott-Chern classes represented by Kähler currents, 19-24.02.2025
• Lecture 20: Kähler currents on complex surfaces with even b₁, 26.02.2025
• Lecture 21: LCK metrics on Kato surfaces, 26.02.2025

Problems sets

• Assignment 1: Hopf surfaces and Kodaira surfaces, 06.01.2024.
• Assignment 2: Morse-Novikov cohomology, 13.01.2024.
• Assignment 3: Harmonic functions, 27.01.2024.
• Assignment 4: Fubini-Study metric and its potential, 14.02.2024.
• Assignment 5: Currents and the Hahn-Banach theorem, 21.02.2024.

• Exam problems
• Personal problem sets, obtained randomly with this program.