Commutative Algebra and Algebraic Geometry II
Lecturers and Teaching Assistants
Prof. Dmitry Gourevitch
Course Schedule and Location
Thursday, 10:15 - 13:00, Ziskind, Rm 155
Field of Study, Course Type and Credit Points
Mathematics and Computer Science: Lecture; Elective; Regular; 4.00 points
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
No final exam or assignment
Estimated Weekly Independent Workload (in hours)
 Algebraic curves and their non-singular models
 Riemann-Roch theorem - elementary approach
 Sheaves, quasi-coherent sheaves, Serre's theorem, coherent sheaves, Nakayama's lemma
 Higher cohomological operations with sheaves. Base change
 Divisors, invertible sheaves, Picard group
 Riemann-Roch theorem and applications.
Upon successful completion of this course students should be able to:
 Describe the basic notions of commutative algebra and algebraic geometry.
 Translate problems from algebra to geometry and vice versa.
 Use powerful algebraic techniques in geometric problems.
 Solve abstract algebraic problems by using acquired geometric intuition.
 Access modern literature in the broad fields of algebra and geometry.
 Atiyah-Macdonalds "Introduction to commutative algebra"
 Eisenbud "Commutative Algebra With a View Toward Algebraic Geometry"
 Kempf "Algebraic varieties"
 A course by A. Gathmann