Toric

Yaël Dillies, Paul Lezeau, Patrick Luo, Michał Mrugała, Justus Springer, Andrew Yang

Lemma 1
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The fibre product of affine schemes is the tensor product of the rings.

Definition 2
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Smooth schemes

Definition 3
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Radical of a group (https://www.jmilne.org/math/CourseNotes/RG.pdf p62)

1 Affine Toric Varieties

1.1 Introduction to Affine Toric Varieties

Definition 4
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Lean declarations

Torus

Definition 5
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Character

Definition 6
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One-parameter subgroup

Definition 7
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Uses

Character lattice

Definition 8
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Uses

One-parameter subgroup lattice

Proposition 9
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Uses

Proposition 1.1.1(a)

Proposition 10
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Uses

Proposition 1.1.1(b)

Definition 11
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Uses

Character eigenspace

Proposition 12
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Uses

Proposition 1.1.2

Definition 13
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Character lattice and one-parameter subgroup pairing

Definition 14
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Uses

Lean declarations

Toric variety

Definition 15
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Uses

\(\Phi _{\mathcal{A}}\)

Definition 16
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Uses

\(Y_{\mathcal{A}}\)

Proposition 17
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Uses

Proposition 1.1.8

Proof ▶
Proposition 18
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Uses

Proposition 1.1.9

Definition 19
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Lean declarations

Toric ideal

Proposition 20
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Lean declarations

Proposition 1.1.11

Proof ▶
Definition 21
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Affine semigroup

Proposition 22
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Uses

Proof ▶
Definition 23
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Torus action on semigroup algebra

Proof ▶
Theorem 25
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Uses

Proof ▶