Wintersemester 2026/2027, Universität des Saarlandes: Complex Geometry.
Aim of the course: to introduce students to the basic theory of complex and Kähler manifolds.
Content: complex atlases, holomorphic tangent and cotangent space, differential forms, sheaves and their cohomology, Dolbeault complex and Dolbeault theorem, Kähler manifolds, Hodge decomposition theorem.
Prerequisites: Linear algebra, complex analysis(=Funktionentheorie).
Registration: Send an email with your full name and Matrikelnummer to me: denisi[add @math.uni-sb.de]
Lectures: Thursday, 16-18, HS IV (E2 4)
Exercise classes: Friday (every two weeks), 14-16. The room has to be defined.
Exam: Oral exam at the end of the semester, to be scheduled individually.
Language of the course: English.
References:
1)"Hodge theory and complex algebraic geometry I", by Claire Voisin.
2)"Complex Geometry: An Introduction", by Daniel Huybrechts.
3)Christian Schnell's notes.
4)Andreas Höring's notes.