WebLet f: X S be a morphism locally of finite type. If S is Noetherian and f is flat, then all fibres have the same dimension. Personally I believe what he wants to say is that the fiber dimension is "locally constant" because his statement could obviously fail when X is not connected. This is the dream theroem you and me are expecting. WebMar 12, 2014 · One of the most commonly cited reasons that flat morphisms are “useful” is that they describe “continuously/smoothly varying families of varieties”. To try and understand what this means, suppose that is of finite type, and is reduced. Then, we can think of as describing a method of piecing together the family of varieties .

Morphisms of toric varieties - Schemes

WebOne should probably also mention the "miracle flatness" theorem: If f: X → Y is finite, X and Y have the same dimension, X is Cohen-Macaulay and Y is regular, then f is flat. As everyone has mentioned above, finite and flat implies locally free, so this theorem can be one useful way to get the flatness hypothesis. Share Cite Improve this answer WebA morphism of schemes is weakly étale or absolutely flat if both and the diagonal morphism are flat. An étale morphism is weakly étale and conversely it turns out that a weakly étale morphism is indeed somewhat like an étale morphism. For example, if is weakly étale, then , as follows from Cotangent, Lemma 91.8.4. prot paladin wrath glyphs

flat module in nLab

Webonly if for each DVR R and morphism Spec R !S sending the closed point of Spec R to f(s), the pullback of f to Spec R is flat at all points lying over x. We will see a proof of this in the projective case soon. Proposition 2. Let f : X !Y be a flat morphism of finite type and suppose Y is locally Noetherian and locally finite-dimensional. WebJul 5, 2016 · Under the dual geometric interpretation of modules as generalized vector bundlesover the space on which RRis the ring of functions, flatness of a module is essentially the local trivialityof these bundles, hence in particular the fact that the fibersof these bundles do not change, up to isomorphism. See prop. below for the precise … Webfiber_generic #. Return the generic fiber. OUTPUT: a tuple \((X, n)\), where \(X\) is a toric variety with the embedding morphism into domain of self and \(n\) is an integer.. The fiber over the base point with homogeneous coordinates \([1:1:\cdots:1]\) consists of \(n\) disjoint toric varieties isomorphic to \(X\).Note that fibers of a dominant toric morphism are … prot paladin wrath spec