Commutative Algebra and Algebraic Geometry

Course info

• Class hours: Monday & Tuesday 14-16.
• Location: BME campus, building H, room 405A
• Office hours: Before or after the Tuesday classes (13.30-14.15 and 16-16.30), or ask in email.

No class on 17/09

For BME students

Neptun code: BMETE91MM01
Credits: 5
Final grade: Homeworks + 2 short midterms

For BSM students

Course title: Commutative Algebra and Algebraic Geometry — CAG
Final grade: Homeworks + 2 short midterms

Documents

• Course description
• Commutative algebra notes (Under construction)
• Algebraic geometry lecture notes by Andreas Gathman

Homework

• HW 1 Due: 23/09
• HW 2 Due: 07/10
• HW 3 Due: 28/10
• HW 4 Due: 11/11
• HW 5 Due: 02/12

Midterms

1. October 15
   Topics: Commutative algebra, prime and maximal ideals, radicals, affine varieties, Hilbert’s Nullstellensatz, Noetherian rings, Hilbert’s basis theorem, Noether-Lasker theorem, Noetherian topological spaces, Noether’s Normalisation Lemma, localisation, sheaf of regular functions
2. November 26
   Topics: prevarieties, gluing, varieties, projective varieties, homogeneous coordinates, Segre embedding, Veronese embedding, Grassmannian variety, birational maps, function field, blow-up, tangent cone

Format: 30 minutes, 2 questions (1 theory + 1 problem very similar to a homework exercise)