||8 credit points
||Moonen, B.J.J. (Universiteit van Amsterdam), Taelman, L. (Universiteit Leiden)
||The goal of the course is to introduce concepts and techniques of algebraic geometry, up to a level where students can begin to study current research literature.
||This is an advanced course on algebraic geometry for students who are already familiar with some basic notions of algebraic geometry. The main focus of the course will be on the geometry of nonsingular curves and surfaces. Chapters 4 and 5 of Hartshorne's book give a good idea of what we are aiming for. Along the way we shall introduce several techniques, such as sheaves and their cohomology. Rather than developing the full theory of schemes we will focus on geometric aspects.
||There will be a weekly 3-hour lecture. As part of their study we expect students to work through exercises on their own initiative. Also we expect them to be willing to independently study material from the literature.
||At the end of the course there will be a take home assignment. After this there is an oral exam.
||As a main reference we shall use Hartshorne's book 'Algebraic Geometry'. This is a classic and we recommend that students get hold of their own copy. In addition to this we shall use bits and pieces from other textbooks, to be announced during the course.
||This is an advanced course, only for students who are already familiar with some basic notions of algebraic geometry, including: affine varieties and their coordinate rings, projective varieties, irreducibility, morphisms of varieties, regular and rational functions, the function field. The mastermath course Algebraic Geometry provides sufficient background to follow this course.
*This is a course offered by WONDER. It is an advanced master and beginning graduate student level course. Students cannot apply for travel costs for this course.
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