منابع مشابه
Piecewise Morphisms of Birational Foliated Varieties
In this article, we study birational varieties with 1-dimensional foliation and induced piecewise morphisms. Let X and Y be smooth complete complex varieties. Consider a birational map f : X · · · → Y . By definition, f is not generally defined all over X. We observe that if X has some one-dimensional foliation, it is possible to extend f to the whole space X as a piecewise morphism (that is, a...
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Smooth toric Fano varieties are classified up to dimension 4. In dimension 2, there are five toric Del Pezzo surfaces: P, P1×P1, and Si, the blowup of P in i points, for i = 1, 2, 3. There are 18 toric Fano 3-folds [2, 20] and 124 toric Fano 4-folds [4, 17]. In higher dimensions, little is known about them and many properties that hold in low dimensions are not known to hold in general. Let X b...
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It is known that any factorization of a local birational morphism f: Spec 5 —» SpecJ? of nonsingular (affine) schemes of arbitrary dimension via other nonsingular schemes must be finite in length. This fact generalizes the classical Local Factorization Theorem of Zariski and Abhyankar, which states that there is a unique such factorization, that given by quadratic transformations, in the surfac...
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We study birational monomial transformations of the form φ(x : y : z) = (ε1x1y1z1 : ε2x2y2z2 : xα3yβ3zγ3), where ε1,ε2 ∈ {−1,1}. These transformations form a group. We describe this group in terms of generators and relations and, for every such transformation φ, we prove a formula, which represents the transformationφ as a product of generators of the group. To prove this formula, we use birati...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2004
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-04-07490-8