Algebraic Geometry

Lecturer: Daniel Galviz & Francisco Villacis

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Content

Week 1:

- Lecture 1: Introduction and basics of category theory

- Lecture 2: Zariski Topology and Affine Varieties

- Lecture 3: Algebraic Varieties and Projective Varieties

Week 2:

- Lecture 4: Sheaves and Stalks

- Lecture 5: Abelian sheaves

- Lecture 6: Sheaves of modules & Coherent Sheaves

Week 3:

- Lecture 7: Schemes

- Lecture 8: Morphisms of schemes

- Lecture 9: Projective morphisms

Week 4:

- Lecture 10: Differentials and Divisors on curves

- Lecture 11: Vector Bundles

- Lecture 12: Sheaf cohomology

This mini course is evaluated with assignments.

Applications are now closed

Lecture Notes

Guest Speakers

Dennis Gaitsgory [Geometric Langlands Correspondence]
Richard Thomas [Spec and Proj] [Slides]
Daniel Galviz [Gromov-Witten Theory and String Theory] [Slides]
Daniel Huybrechts [Algebraic Geometry of Kähler manifolds] [Slides]
Artan Sheshmani [Super Gromov-Witten invariants on almost Kähler varieties]
Lothar Göttsche [Hilbert schemes of points on surfaces] [Slides]
Martinj Kool [Algebraic geometry and Vafa-Witten theory] [Slides]
Claire Voisin [Variations of Hodge structures and geometric applications] [Slides]
Yalong Cao [Gopakumar-Vafa type invariants of Calabi-Yau 4-folds] [Slides]
Catherine Cannizzo [Homological Mirror symmetry] [Slides]

Exercise sheets

LITERATURE

Robin Hartshorne, Algebraic Geometry
D. Galviz and F. Villacis, Physics Latam: Lectures on Algebraic Geometry
Alexander Grothendieck, Elements of Algebraic Geometry
Ravi Vakil, The Rising Sea: Foundations of Algebraic Geometry
Harris and Phillip Griffiths, Principles of Algebraic Geometry
Igor Shafarevich, Basic Algebraic Geometry 1 & 2

successfully passed students

Allan Hurtado 🇬🇹
(University of San Carlos of Guatemala, GT)

Isaac Mendez 🇲🇽
(Universidad Autónoma del Estado de Mexico, MX)

Juan Morales 🇨🇴
(Universidad de los Andes, CO)

Franco Rufolo 🇦🇷
(Universidad de Buenos Aires, AR)

Daniel Reyes 🇲🇽
(Universidad Nacional Autónoma de México, MX)

Ronald Urrutia 🇧🇷
(Universidade de São Paulo, BR)

Heldert Villegas 🇨🇴
(Universidad Nacional de Colombia, CO)

Guest SPEAKERs

Catherine Cannizzo

UC- Berkeley

Yalong Cao
RIKEN Institute

Alexander Cruz

UNAL

Dennis Gaitsgory
Harvard U.

Lothar Göttsche
ICTP

Mark Gross

Cambridge U.

Daniel Huybrechts
Bonn University

Martijn Kool

Utrecht University.

Pranav Pandit
ICTS-TIFR

Richard Thomas
Imperial College London

Artan Sheshmani
Harvard U. & BIMSA Tsinghua U.

Claire Voisin
IMJ-Paris Rive Gauche

Lecturers

Francisco Villacis

(Pure Mathematics University of Waterloo, CA)

Lecturer & Organizer
Daniel Galviz
YMSC (Tsinghua University)
ICTS (Tata Institute of Fundamental Research, IN)

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