Course Identification
Commutative Algebra and Algebraic Geometry II
Lecturers and Teaching Assistants
Prof. Dmitry Gourevitch
Course Schedule and Location
Second Semester
Thursday, 10:15 - 13:00, Jacob Ziskind Building, Rm 155
20/04/2023
Field of Study, Course Type and Credit Points
Mathematics and Computer Science: Lecture; Elective; Regular; 4.00 points
Prerequisites
A semester course in algebraic geometry: algebraic varieties, morphisms, commutative rings and modules over them, dimension, smoothness.
Attendance and participation
Grade Breakdown (in %)
maybe there will be an interim exam
Evaluation Type
No final exam or assignment
Estimated Weekly Independent Workload (in hours)
Syllabus
[1] Algebraic curves and their non-singular models
[2] Riemann-Roch theorem - elementary approach
[3] Sheaves, quasi-coherent sheaves, Serre's theorem, coherent sheaves, Nakayama's lemma
[4] Cohomologies
[5] Higher cohomological operations with sheaves. Base change
[6] Divisors, invertible sheaves, Picard group
[7] Riemann-Roch theorem and applications.
Learning Outcomes
Upon successful completion of this course students should be able to:
[1] Describe the basic notions of commutative algebra and algebraic geometry.
[2] Translate problems from algebra to geometry and vice versa.
[3] Use powerful algebraic techniques in geometric problems.
[4] Solve abstract algebraic problems by using acquired geometric intuition.
[5] Access modern literature in the broad fields of algebra and geometry.
Reading List
[1] Atiyah-Macdonalds "Introduction to commutative algebra"
[2] Eisenbud "Commutative Algebra With a View Toward Algebraic Geometry"
[3] Kempf "Algebraic varieties"
[4] A course by A. Gathmann
http://www.mathematik.uni-kl.de/~gathmann/class/alggeom-2002/main.pdf