Maximal algebraic subgroups of the Cremona group of three variables—Imprimitive algebraic subgroups of exceptional type

Maximal Algebraic Subgroups of the Cremona Group of Three Variables Imprimitive Algebraic Subgroups of Exceptional Type

Enriques and Fano [4], [5] classified all the maximal connected algebraic subgroups of Cr3. Our aim is to give modern and rigorous proofs to their results. In [10], we studied the primitive subgroups. In this paper, we deal with exceptional imprimitive groups. The imprimitivity is an analytic notion. The natural translation of the imprimitivity in algebraic geometry is the de Jonquieres type op...

Finite Subgroups of Algebraic Groups

0. Introduction 1105 1. Constructible families 1111 2. Genericity for finite subgroups 1116 3. Finite groups of Lie type 1119 4. Basic nonconcentration estimate 1122 5. Finite subgroups of abelian varieties 1126 6. Orders of conjugacy classes and centralizers 1127 7. Regular semisimple and unipotent elements 1129 8. Minimal unipotent elements 1134 9. Frobenius map 1140 10. Traces in the basic c...

Observable subgroups of algebraic monoids

A closed subgroup H of the affine, algebraic group G is called observable if G/H is a quasi-affine algebraic variety. In this paper we define the notion of an observable subgroup of the affine, algebraic monoid M . We prove that a subgroup H of G is observable in M if and only if H is closed in M and there are “enough” H-semiinvariant functions in k[M ]. We show also that a closed, normal subgr...

Finite abelian subgroups of the Cremona group of the plane

Maximal Integral Forms of the Algebraic Group G 2 Deened by Nite Subgroups

We coin the notation maximal integral form of an algebraic group generalizing Gross' notion of a model. We extend the mass formula given by Gross to our context. For the nite Lie primitive subgroups of G 2 there are unique maximal integral forms deened by them.