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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
- I.1.1-I.1.4; all H = 1
- I.1.5; H = 1
- I.1.6; H = 1
- I.1.7; H = 1
- I.1.8; H = 1
- I.1.9; H = 1
- I.1.10; H = 2, V = 2
- I.1.11
- I.1.12
Hartshorne I.2
- I.2.1-I.2.5; #4 has H = 2, V = 3
- I.2.6; H = 2, V = 3
- I.2.7-I.2.10; all H = 2, #8 has V = 5
- I.2.11; H = 2, V = 4
- I.2.12; H = 1
- I.2.13
- I.2.14
Hartshorne I.3
Hartshorne Chapter II[]
Hartshorne II.1
- II.1.1; H = 1
- II.1.2; H=1
- II.1.3
- II.1.4
- II.1.5
- II.1.6; H = 2, V = 2
- II.1.7
- II.1.8
- II.1.9
- II.1.10; H = 1
- II.1.11; H = 2, V = 2
- II.1.12
- II.1.13
- II.1.14; H = 1
- II.1.15; H = 1
- II.1.16; H = 1
- II.1.17
- II.1.18
- II.1.19
- II.1.20
- II.1.21
- II.1.22
- II.1.23
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