Algebraic Geometry

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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

I.3.20

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