Forim@ge Books > Geometry And Topology > Abelsche Funktionen und algebraische Geometrie MAg by Conforto F.

Abelsche Funktionen und algebraische Geometrie MAg by Conforto F.

By Conforto F.

Show description

Read or Download Abelsche Funktionen und algebraische Geometrie MAg PDF

Best geometry and topology books

Grassmannians and Gauss Maps in Piecewise-Linear and Piecewise-Differential Topology

The publication explores the opportunity of extending the notions of "Grassmannian" and "Gauss map" to the PL type. they're individual from "classifying house" and "classifying map" that are basically homotopy-theoretic notions. The analogs of Grassmannian and Gauss map outlined comprise geometric and combinatorial details.

Extra info for Abelsche Funktionen und algebraische Geometrie MAg

Example text

Z through some point x E X \ {0} = Xa,. We may thus replace x with the orbit base point x,,,. By hypothesis, the unicity of 7-0 is valid in every affine open subvariety X,, that includes 0, so it is valid in X u . For the asserted correspondence between faces and invariant irreducible closed subvarieties, we consider such an A L) X , with A := A \ F # 8. Then A = UTEa,(A n X,) implies the equality dim(A n X,) = dimA for some face T E 8u. Again by induction hypothesis, there is a face TO 5 T with A n X, = V(TO) = TO), the closure being taken in X,; moreover, TO) is open in AnX, and hence, has the same dimension.

For any two cones u,u’ E A, the intersection X u n Xu, is a T-invariant affine open subspace of X, and thus X u n Xu) = X, with a cone r E A. Since X is separated, a one-parameter subgroup X E Y(T) has at most one limit 41 X(0) E X . 8 (2), the following holds: I - n N = {V E N ; x,(o) E xunXul} Xu}n {V =(anN)n(dnN). = {V E N ; X,(o) E E N ; X,(O) E Xul} This readily implies that I- = a n a’. 3. An (N-lattice) fan in Nw is a finite non-empty set A of (strongly convex) N-cones satisfying (1) r 5 u E A j T E A ; (2) a, a’ E A ----7- a n a’ 5 0,a’; in particular, u n a’ E A.

8, we know that t o each a6ne toric variety, say U , corresponds a unique N-cone u = uu such that U = X u . To the general toric variety X, we may thus associate the following collection of N-cones: A := A(X) := {u = m~ E Ob(6CN) ; U QI X} , where U runs through the affine open toric subvarieties of X. For any two cones u,u’ E A, the intersection X u n Xu, is a T-invariant affine open subspace of X, and thus X u n Xu) = X, with a cone r E A. Since X is separated, a one-parameter subgroup X E Y(T) has at most one limit 41 X(0) E X .

Download PDF sample

Rated 4.44 of 5 – based on 19 votes