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Algebraic Geometry

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Welcome to the Algebraic Geometry mini wiki at Scratchpad!

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Algeo is a wiki for students learning algebraic geometry to discuss problems, solutions, and general perspective on the subject.

Announcements

  • No seminar planned for February 20th.

Problem selections Below is a list of problems from Hartshorne. The notation (h,v) gives the height and volume of the problem. These wont be well defined numbers but here's an attempt to define them. A Hartshorne exercise E1 is in the support of another E2 if there is a solution to E2 that applies E1. The height of a problem is 1 + the cardinality of its support. Define extended support as follows. If height(E) = 1, then the extended support is just the support. If height(E) >1, then the extended support of E is the union of the support of E with the extended supports of all the problems in the support of E. The volume is 1 + cardinality of its extended support. The volume is 1 iff the height is 1. When the height is 2 the volume can be much larger.


Hartshorne Chapter I

Hartshorne I.1

Hartshorne I.2

Hartshorne I.3

Hartshorne Chapter II

Hartshorne II.1

Hartshorne II.2

  • II.2.1; H = 1
  • II.2.2; H = 2, V = 2
  • II.2.3; H = 1
  • II.2.4; H = 4, V = ...
  • II.2.5
  • II.2.6
  • II.2.7
  • II.2.8
  • II.2.9
  • II.2.10
  • II.2.11
  • II.2.12
  • II.2.13
  • II.2.14
  • II.2.15
  • II.2.16
  • II.2.17
  • II.2.18
  • II.2.19

Hartshorne II.3

  • II.3.1
  • II.3.2
  • II.3.3
  • II.3.4
  • II.3.5
  • II.3.6
  • II.3.7
  • II.3.8
  • II.3.9
  • II.3.10
  • II.3.13; H = 2, V = ....
  • II.3.12
  • II.3.13; H = 1, V = 1
  • II.3.14
  • II.3.15
  • II.3.16
  • II.3.17
  • II.3.18
  • II.3.19
  • II.3.20
  • II.3.21
  • II.3.22
  • II.3.23

Hartshorne II.4

  • II.4.1; H = 3, V = ...
  • II.4.2; H = 2, V = ...
  • II.4.3; H = 3, V = ...
  • II.4.4; H = 2, V = ..., (no part c)
  • II.4.5; H = 2, V = ...
  • II.4.6; H = 2, V = ...
  • II.4.7
  • II.4.8; H =2, V = ...
  • II.4.9
  • II.4.10
  • II.4.11
  • II.4.12

Hartshorne II.5

  • II.5.1
  • II.5.2
  • II.5.3
  • II.5.4
  • II.5.5
  • II.5.6
  • II.5.7
  • II.5.8
  • II.5.9
  • II.5.10
  • II.5.11
  • II.5.12
  • II.5.13
  • II.5.14
  • II.5.15
  • II.5.16
  • II.5.17
  • II.5.18

Hartshorne II.6

  • II.6.1
  • II.6.2
  • II.6.3
  • II.6.4
  • II.6.5
  • II.6.6
  • II.6.7
  • II.6.8
  • II.6.9
  • II.6.10
  • II.6.11
  • II.6.12

Hartshorne II.7

  • II.7.1
  • II.7.2
  • II.7.3
  • II.7.4
  • II.7.5
  • II.7.6
  • II.7.7
  • II.7.8
  • II.7.9
  • II.7.10
  • II.7.11
  • II.7.12
  • II.7.13
  • II.7.14

Hartshorne II.8

  • II.8.1
  • II.8.2
  • II.8.3
  • II.8.4
  • II.8.5
  • II.8.6
  • II.8.7
  • II.8.8

Hartshorne II.9

  • II.9.1
  • II.9.2
  • II.9.3
  • II.9.4
  • II.9.5
  • II.9.6

Hartshorne Chapter III

Hartshorne III.1

  • III.4.No problems!

Hartshorne III.2

  • III.2.1
  • III.2.2
  • III.2.3
  • III.2.4
  • III.2.5
  • III.2.6
  • III.2.7

Hartshorne III.3

  • III.3.1
  • III.3.2
  • III.3.3
  • III.3.4
  • III.3.5
  • III.3.6
  • III.3.7
  • III.3.8

Hartshorne III.4

  • III.4.1
  • III.4.2
  • III.4.3
  • III.4.4
  • III.4.5
  • III.4.6
  • III.4.7
  • III.4.8
  • III.4.9
  • III.4.10
  • III.4.11


Hartshorne III.5

  • III.5.1
  • III.5.2
  • III.5.3
  • III.5.4
  • III.5.5
  • III.5.6
  • III.5.7
  • III.5.8
  • III.5.9
  • III.5.10

Hartshorne III.6

  • III.6.1
  • III.6.2
  • III.6.3
  • III.6.4
  • III.6.5
  • III.6.6
  • III.6.7
  • III.6.8
  • III.6.9
  • III.6.10

Hartshorne III.7

  • III.7.1
  • III.7.2
  • III.7.3
  • III.7.4

Hartshorne III.8

  • III.8.1
  • III.8.2
  • III.8.3
  • III.8.4

Hartshorne III.9

  • III.9.1
  • III.9.2
  • III.9.3
  • III.9.4
  • III.9.5
  • III.9.6
  • III.9.7
  • III.9.8
  • III.9.9
  • III.9.10
  • III.9.11

Hartshorne III.10

  • III.10.1
  • III.10.2
  • III.10.3
  • III.10.4
  • III.10.5
  • III.10.6
  • III.10.7
  • III.10.8
  • III.10.9

Hartshorne III.11

  • III.11.1
  • III.11.2
  • III.11.3
  • III.11.4
  • III.11.5
  • III.11.6

Hartshorne III.12

  • III.12.1
  • III.12.2
  • III.12.3
  • III.12.4
  • III.12.5
  • III.12.6

Hartshorne Chapter IV

Hartshorne IV.1

  • IV.1.1
  • IV.1.2
  • IV.1.3
  • IV.1.4
  • IV.1.5
  • IV.1.6
  • IV.1.7
  • IV.1.8
  • IV.1.9
  • IV.1.10

Hartshorne IV.2

  • IV.2.1
  • IV.2.2
  • IV.2.3
  • IV.2.4
  • IV.2.5
  • IV.2.6
  • IV.2.7

Hartshorne IV.3

  • IV.3.1
  • IV.3.2
  • IV.3.3
  • IV.3.4
  • IV.3.5
  • IV.3.6
  • IV.3.7
  • IV.3.8
  • IV.3.9
  • IV.3.10
  • IV.3.11
  • IV.3.12

Hartshorne IV.4

  • IV.4.1
  • IV.4.2
  • IV.4.3
  • IV.4.4
  • IV.4.5
  • IV.4.6
  • IV.4.7
  • IV.4.8
  • IV.4.9
  • IV.4.10
  • IV.4.11
  • IV.4.12
  • IV.4.13
  • IV.4.14
  • IV.4.15
  • IV.4.16
  • IV.4.17
  • IV.4.18
  • IV.4.19
  • IV.4.20
  • IV.4.21
  • IV.4.22

Hartshorne IV.5

  • IV.5.1
  • IV.5.2
  • IV.5.3
  • IV.5.4
  • IV.5.5
  • IV.5.6
  • IV.5.7

Hartshorne IV.6

  • IV.6.1
  • IV.6.2
  • IV.6.3
  • IV.6.4
  • IV.6.5
  • IV.6.6
  • IV.6.7
  • IV.6.8
  • IV.6.9

Hartshorne Chapter V

Hartshorne V.1

  • V.1.1
  • V.1.2
  • V.1.3
  • V.1.4
  • V.1.5
  • V.1.6
  • V.1.7
  • V.1.8
  • V.1.9
  • V.1.10
  • V.1.11
  • V.1.12

Hartshorne V.2

  • V.2.1
  • V.2.2
  • V.2.3
  • V.2.4
  • V.2.5
  • V.2.6
  • V.2.7
  • V.2.8
  • V.2.9
  • V.2.10
  • V.2.11
  • V.2.12
  • V.2.13
  • V.2.14
  • V.2.15
  • V.2.16
  • V.2.17

Hartshorne V.3

  • V.3.1
  • V.3.2
  • V.3.3
  • V.3.4
  • V.3.5
  • V.3.6
  • V.3.7
  • V.3.8

Hartshorne V.4

  • V.4.1
  • V.4.2
  • V.4.3
  • V.4.4
  • V.4.5
  • V.4.6
  • V.4.7
  • V.4.8
  • V.4.9
  • V.4.10
  • V.4.11
  • V.4.12
  • V.4.13
  • V.4.14
  • V.4.15

Hartshorne V.5

  • V.5.1
  • V.5.2
  • V.5.3
  • V.5.4
  • V.5.5
  • V.5.6
  • V.5.7
  • V.5.8

Hartshorne V.6

  • V.6.1
  • V.6.2

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