19:53
01.05 Functions on affine varieties
16:41
01.01 Affine varieties
18:26
01.02 Properties of vanishing sets
18:21
01.04 Consequences of the Nullstellensatz
18:37
01.03 Correspondence of affine varieties and ideals via the Nullstellensatz
12:56
01.06 Affine subvarieties and relative vanishing ideals
37:07
00 Introduction
08:21
02.05 Irreducible decompositions of affine varieties
16:42
01.07 Products of affine varieties
05:51
A02.2 Connected components
12:39
02.01 Definition of the Zariski topology
25:11
02.04 Noetherian spaces and irreducible decompositions
15:18
02.03 Irreducible affine varieties
11:35
02.02 Irreducible and connected topological spaces
08:43
A02.1 Basics of topology
11:32
03.03 Distinguished open subsets
26:31
02.10 Hypersurfaces and unique factorization domains
10:15
03.02 Properties of regular functions
17:45
02.08 Dimension of affine varieties
08:09
03.05 Regular functions via localizations
12:56
02.07 Dimension of topological spaces
19:00
02.06 Connected components of affine varieties
21:52
02.09 Dimension theory of reducible spaces
19:22
03.04 Regular functions on distinguished open subsets
19:42
03.01 Definition of regular functions
06:27
04.05 Products of affine varieties revisited
09:39
04.03 Morphisms between affine varieties
14:30
03.09 Stalks of affine varieties
13:02
04.01 Ringed spaces and their morphisms
09:17
03.08 Stalks of presheaves
22:10
03.07 Presheaves and sheaves
09:02
03.06 Extending regular functions over sets of high codimension
17:40
04.04 Morphisms of affine varieties via coordinate rings
06:56
A03.1 Categories
08:43
04.02 Properties of morphisms of ringed spaces
15:20
05.06 Separatedness and the definition of varieties
17:36
05.04 Basic properties and constructions of prevarieties
06:22
05.03 Gluing finite collections of prevarieties
18:01
05.05 Products of prevarieties
07:24
04.07 Open subsets of affine varieties
20:21
05.02 Gluing two prevarieties
08:00
05.01 Prevarieties
12:00
06.01 Projective space and homogeneous coordinates
05:20
A05.1 Digression - Locally closed sets and constructible sets
10:39
04.06 Correspondence of affine varieties and finitely generated reduced K algebras
10:37
06.08 Homogeneous coordinate rings, projective subvarieties and the Zariski topology
16:57
06.06 Cones and projective varieties
19:32
06.07 The projective Nullstellensatz
15:37
06.04 Homogeneous ideals
12:27
06.09 Homogenization and dehomogenization
12:12
06.05 Projective varieties
06:18
06.10 Topological properties of projective space
16:27
06.11 The projective closure
11:34
06.03 Homogeneous polynomials and graded rings
11:37
06.02 Affine space as a subset of projective space
13:04
06.12 Projective hypersurfaces
29:00
07.03 Projecting from a point
25:10
07.05 Closed maps
19:27
08.05 Grassmannians as projective varieties
17:14
07.07 The Veronese embedding
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