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Download e-book for iPad: Birational Geometry of Degenerations by Robert Friedman

By Robert Friedman

ISBN-10: 3764331119

ISBN-13: 9783764331115

This quantity offers new advancements within the thought
of degenerations. The unifying subject is the applica-
tion of options from the birational geometry of
threefolds. one of the purposes of this research are
partial compactifications of moduli areas of algebraic
varieties and perception into the geometry of tender
varieties.

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Additional info for Birational Geometry of Degenerations

Example text

Define a cohomological correspondence ! uC : ( j T g )∗ (iC1 TC1 )! LC1 −→ T 1 (iC2 TC2 )! 1), and the direct image with compact support is defined by duality). Finally, write −1 NC = [K(2) N : h2 K h2 ∩ Nnr (Af )]. 3 The coefficient uC1 ,C2 in the above matrix is equal to NC uC , C where the sum is taken over the set of C ∈ CP such that Tg (C ) = C1 and T1 (C ) = C2 . 5). 5 of [P2], and it is true as well for the Shimura varieties considered here. 7. 5. , that G is not an orthogonal group). Fix an algebraic closure F of Fp .

UC : ( j T g )∗ (iC1 TC1 )! LC1 −→ T 1 (iC2 TC2 )! 1), and the direct image with compact support is defined by duality). Finally, write −1 NC = [K(2) N : h2 K h2 ∩ Nnr (Af )]. 3 The coefficient uC1 ,C2 in the above matrix is equal to NC uC , C where the sum is taken over the set of C ∈ CP such that Tg (C ) = C1 and T1 (C ) = C2 . 5). 5 of [P2], and it is true as well for the Shimura varieties considered here. 7. 5. , that G is not an orthogonal group). Fix an algebraic closure F of Fp . Let V ∈ Ob RepG .

Then, for every z ∈ (RE/Q Gm,Q ), µ(z) = (z, 1)Ip 0 0 (1, z)Iq . 2 Let p ∈ {1, . . , n}. Define a cocharacter µp : Gm,E −→ GE by µp (z) = (z, 1)Ip 0 (1, z)In−p . 2 PARABOLIC SUBGROUPS Let G be a connected reductive algebraic group over Q. Fix a minimal parabolic subgroup P0 of G. Remember that a parabolic subgroup of G is called standard if it contains P0 . Fix a Levi subgroup M0 of P0 . Then a Levi subgroup M of G will be called standard if M is a Levi subgroup of a standard parabolic subgroup and M ⊃ M0 .

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Birational Geometry of Degenerations by Robert Friedman


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