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Objectives

General goals: to acquire basic notions and skills in algebraic geometry.

Specific goals:

Knowledge and comprehension: at the end of the course the student will have learnt basic results on Hodge Theory and sheaf cohomology,

as applied to algebraic varieties.

Applied knowledge and comprehension: at the end of the course the student will be able to understand and appreciate part of the current literature on complex algebraic geometry.

Critical development: the student will appreciate the interaction between different fields such as differential geometry, global analysis, algebraic topology and algebaric geometry.

Communication skills: the ability to make a clear presentation of parts of the theory

introduced in the course.

Learning skills: the knowledge acquired will be useful in studying more specialized courses in algebraic and complex geometry.

### Channels

### NESSUNA CANALIZZAZIONE

### KIERAN GREGORY O'GRADY Teacher profile

#### Programme

Affine and projective varieties. Holomorphic functions of several variables. Complex manifolds. Vector bundles. Differential forms on complex manifolds. Harmonic forms. Kaehler manifolds. Kaehler identities. Hodge decomposition, Lefschetz decomposition. Hodge-Riemann bilinear relations. Sheaf cohomology. Period map. Mixed Hodge structure on a smooth quasi-projective variety.

#### Adopted texts

Claire Voisin: Hodge theory and complex algebraic geometry, vols I and II.

Jean-Pierre Demailly: Complex analytic and differential geometry. (Freely available on the authors' website)

#### Prerequisites

The course Istituzioni di Geometria Superiore of the laurea magistrale

#### Study modes

Classroom lectures.

#### Exam modes

The exam is oral. In order to pass the exam (the minimum score is 18/30) the student is required to know the main theoretical results, and to be able to solve simple exercises. In order to get the maximum vote, i.e. 30/30 e lode, the student is required to have a deep knowledge of the theoretical results, and to be able to solve difficult exercises.

Exam reservation date start | Exam reservation date end | Exam date |
---|---|---|

22/10/2018 | 14/06/2019 | 17/06/2019 |

22/10/2018 | 23/07/2019 | 25/07/2019 |

22/10/2018 | 01/09/2019 | 03/09/2019 |

22/10/2018 | 10/09/2019 | 12/09/2019 |

22/10/2018 | 22/01/2020 | 24/01/2020 |

- Academic year: 2018/2019
- Curriculum: Algebra e Geometria
- Year: First year
- Semester: Second semester
- SSD: MAT/03
- CFU: 6

- AttivitÃ formative caratterizzanti
- Ambito disciplinare: Formazione teorica avanzata
- Lecture (Hours): 48
- CFU: 6.00
- SSD: MAT/03