By Conforto F.

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Geometry, mechanics, and dynamics: volume in honor of the 60th birthday of J.E. Marsden

Jerry Marsden, one of many world’s pre-eminent mechanicians and utilized mathematicians, celebrated his sixtieth birthday in August 2002. the development was once marked by way of a workshop on “Geometry, Mechanics, and Dynamics”at the Fields Institute for learn within the Mathematical Sciences, of which he wasthefoundingDirector.

Extra resources for Abelsche Funktionen und algebraische Geometrie MAg

Example text

Proof. 2, we proceed by induction on d := dima. For d = 0 , there is nothing to prove since then a = 0,so X , = 0,= V, = T because of o" = MR. 9, T-objects like orbits, invariant irreducible closed subvarieties, and affine open invariant subvarieties in X u correspond to the respective T,-objects in 2, via Y ++ Y n 2, and vice versa. For convenience, we fix a closed equivariant embedding X ct C‘ given by the character functions xi = xp’ E Sx corresponding to a system of non-zero generators p l , .

P‘ of E also generate the corresponding cone y, the converse need not be true, even if the generating vectors of the cone are primitive; cf. 2 (2). 4. For the semigroup E, := y n M cut out by a strongly convex cone y, there is a canonical minimal system of generators, sometimes called a Hilbert basis: It is the set E \ (E + 8 ) of indecomposable elements in E , with E := E \ (0). In the two-dimensional case, it consists of those primitive lattice vectors p a which lie on the boundary of the (unbounded) “polyhedron” K := conv(8).

N} as above) are cyclic quotients Cn/Gj. There is an isomorphism P(a) z Pn/G(a) with G(a) := Cai acting coordinatewise on P,, so in particular, P(1,. . ,1) equals P,. Moreover, the description P, E (C"+')/D given above generalizes t o the weighted projective space if one replaces the diagonal 1-subtorus D c (C*)n+l with D(a) := {t" = ( P o , . , t a n ); t E C*}. 5 ny=o Secondly, there is a similar equivalence of suitable categories (cf. 7); see (3) below. 6. (1) For each cone c E A, there exists an associated orbit 0, := T*A,(O), where v E a ' .