Mathematics 200911

[GH] Griffiths, P., Harris, J., Principles of Algebraic Geometry, Wiley-Interscience, New
York (1978).

20091105 "The adventure begins..."
[GH] pg 1
Morita, Geometry of Differential Forms pg 57
Lang, Algebra pg 121
Morita, pg 57
Lang, pg 601-603, 609
Morita, pg 58
[GH] pg 2-8
Reference: Lang, pg 190 symmetric polynomials and elementary symmetric polynomials, 192 discriminant
Reference: Hatcher, Algebraic Topology, pg 56 covering space, 61 sheets
[GH] pg 9
Reference: Lang, pg 200-202, resultant
[GH] pg 10
Lang, pg 110, local ring, 205-209 Weierstrass preparation theorem, Weirerstrass polynomial
[GH] pg 10
Note: Lang, pg 212 has a reference to Griffiths and Harris.
[GH] pg 11

20091106
[GH] pg 11 Weak Nullstellensatz
Lang, pg 200-202, resultant, 111-113, relatively prime and so on
Joe Harris, Algebraic Geometry: A First Course

20091107
Harris
PlanetMath.org, resultant
[GH] pg 11 Weak Nullstellensatz
Reference: PlanetMath.org, resultant
Reference: Lang, pg 179
[GH] pg 9

20091108 "Friends boost SPIRIT"
[GH] pg 12-14

20091109
Harris, pg 4-5
[GH] pg 15
Discussion with Arash

20091118
Jean-Pierre Demailly, Complex Analytic and Differential Geometry, pg 7-9
Morita, pg 62 Exterior algebra, pg 63
Reference: Morita, pg 59 exterior product is another name for wedge product
Demailly, pg 9 Contraction by a tangent vector

20091122
Demailly, pg 9 Exterior derivative
Wikipedia, section of a fiber bundle
Wikipedia, differential form
Demailly, pg 9

20091123
Index: Lang, pg 511, 731 alternating multilinear map, 511 alternating form, 733 exterior product
Lang, pg 514 Prop 4.6
Lang, pg 731
Reference: Lang, pg 601 tensor product
Demailly, pg 9
Wikipedia, differential form
Wikipedia, exterior algebra -> alternating multilinear forms

20091124
A bunch of confusion happens when trying to put together different references...
Morita, pg 62
Some clarity occurs...
Lang, pg 514, 515
Wikipedia, exterior algebra -> alternating multilinear forms
Spivak, A Comprehensive Introduction to Differential Geometry, Volume I, pg 201 alternating multilinear forms
Spivak, pg 204
Spivak, Calculus on Manifolds, pg 78-79
Spivak, pg 204, 116

20091125 "Early Morning"
Spivak, pg 107 tensors

20091125 "Afternoon"
Spivak, pg 107
Lang, pg 65 Natural transformation, 54 morphisms and so on, 57 forming a new category where the objects are morphisms of a given category, 62 functors
Spivak, pg 130
Spivak, pg 63 tangent bundle

20091126 "Midnight"

20091126 "Morning"
Spivak, pg 69-72, 77, 82 section of a bundle, 108 dual bundle, 109 dual of a section acting on the section
Spivak, pg 76, 73 bundle map

20091127 "1AM"
Spivak, pg 67

20091127
Spivak, pg 67-69, 73
Reference: Spivak ConM, pg 16, 20 2-3 Theorem (3)
Spivak, pg 74
Reference: Spivak, pg 66
Spivak, pg 74-80

20091128
Gunning, Introduction to Holomorphic Functions of Several Variables pg 1-3
[GH] pg 34-49(?)

No comments:

Let me know what you think!