Misha Verbitsky

Instituto Nacional de Matemática Pura e Aplicada

Variations of Hodge Structures

Sala 236, Tuesdays, Wednesdays 17:00-18:30, January-February 2024

Slides:

• Lecture 1: Hodge structures (January 2).
• Lecture 2: Period maps and Torelli theorems (January 3).
• Lecture 3: Gauss-Manin local system and Griffiths transversality (January 10).
• Lecture 4: Deligne-Griffiths-Schmid fixed part theorem (January 17).
• Lecture 5: Deligne's semisimplicity theorem (January 24).
• Lecture 6: Mumford-Tate group (January 31).
• Lecture 7: Noether-Lefschetz theorem (February 7).
• Lecture 8: Lefschetz pencils (February 14).
• Lecture 9: Picard-Lefschetz formula (February 21).
• Lecture 10: The proof of Noether-Lefschetz theorem (February 28).

Assignments

• Assignment 1: Hodge decomposition on a torus (January 2).
• Assignment 2: Isotrivial elliptic fibrations (January 9).
• Assignment 3: Polarized Hodge structures (January 16).