Equivariant Embeddings of Algebraic Groups

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Page 1 and 2:
c○ Copyright by David Charles Mur
Page 3 and 4:
Abstract We classify embeddings of
Page 5 and 6:
Acknowledgements This thesis would
Page 7 and 8:
Chapter 1 Introduction A basic prob
Page 9 and 10:
x i ≠ 0} for i = 0, 1, 2, the one
Page 11 and 12:
complement of U in G/H. Remark 1 ([
Page 13 and 14:
G. The wonderful compactification o
Page 15 and 16:
X is to use one-parameter subgroups
Page 17 and 18:
Chapter 2 Toric varieties and group
Page 19 and 20:
Proposition 3 ([28], Proposition I.
Page 21 and 22:
and every toric variety for T arise
Page 23 and 24: To see this, suppose D is a T -stab
Page 25 and 26: Conversely, every subdivision of C
Page 27 and 28: 0 : 0 : 1 : 1], [0 : 0 : 0 : 1 : 1]
Page 29 and 30: Mumford’s embedding is constructe
Page 31 and 32: Moreover, Ind(X) is a G-embedding,
Page 33 and 34: the T -action with respect to the c
Page 35 and 36: from X with a line bundle from the
Page 37 and 38: G/B × G/B − corresponding to the
Page 39 and 40: since G (and hence G × G) is semi-
Page 41 and 42: 1. There is a finite-dimensional G-
Page 43 and 44: the following (obviously) commutati
Page 45 and 46: Now, to prove the claim, by Lemma 7
Page 47 and 48: ational polyhedral cone in X ∗ (T
Page 49 and 50: ⋃ P ⊃T P • (σ ∩ ∆ P (T )
Page 51 and 52: Section 3.2.3, is a uniqueness theo
Page 53 and 54: Therefore, the classification of af
Page 55 and 56: For each k-point g of G, we have ma
Page 57 and 58: is over a finite set of integers J.
Page 59 and 60: i ≥ 0, 〈χ ij , γ (0,1) 〉 =
Page 61 and 62: Lemma 12. If γ 1 , γ 2 ∈ X ∗
Page 63 and 64: an integrally closed left-invariant
Page 65 and 66: of the subalgebras A Γ(X,x0 ) ⊂
Page 67 and 68: on varieties discussed in this sect
Page 69 and 70: Proof. Let Γ be a strongly convex
Page 71 and 72: that Γ(X, [I 2 , (1, 1)]) GL 2 = {
Page 73: References [1] A. Bialynicki-Birula
Page 77: Vita David Charles Murphy was born
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