A Morphism Of Algebraic Varieties (over A Field Characteristic 0) Is Monomial If It Can Locally Be Represented In E'tale Neighborhoods By A Pure Monomial Mappings. The Book Gives Proof That A Dominant Morphism From A Nonsingular 3-fold X To A Surface S Can Be Monomialized By Performing Seq...
the elimination of the z leads to one set of differential algebraic equations (hence, with no inequations ) if the projection map along z is a finite morphism of algebraic varieties; that is, if the differential algebra which defines the system is integral over a suitable differential subalgebr...
This chapter is concerned mainly with the dimension-theoretical analysis of morphisms between varieties. This involves substantially more commutative algebra than has been used up to now. Thus, Section 1 establishes Noether鈥檚 Normalization Theorem, which is used for reducing some of the required ...
摘要:In the note under review we are interested to estimate the inseparable degree of a morphisms between algebraic varieties. We prove: Theorem: Let g:X→Y be a generically finite dominant morphism of irreducible algebraic varieties. There exist finitely many codimension one subvarieties Z 1 ,...
Mori Birational geometry of algebraic varieties Cambridge Tracts in Mathematics, vol. 134, Cambridge University Press, Cambridge (1998) MR 2000b:14018 Google Scholar [18] Y. Namikawa Extension of 2-forms and symplectic varieties J. Reine Angew. Math., 539 (2001), pp. 123-147 MR 1863856 (...
there can be varieties which are not isomorphic over $k'$ but which become isomorphic when base changed to $k$). What it consists of is affine varieties $X$ over $k$ which happen to be the base change of an affine variety $X'$ over $k'$; a choice of such an affine variety is...
In this paper we generalize the arithmetic Grothendieck-Riemann-Roch theorem to the case of general projective morphisms between regular arithmetic varieties. To this end we rely on the theory of generalized analytic torsion developed by the authors....
Define Morphisms. Morphisms synonyms, Morphisms pronunciation, Morphisms translation, English dictionary definition of Morphisms. n. In mathematical category theory, a generalization or abstraction of the concept of a structure-preserving function. Ameri
Given two nonsingular real algebraic varieties V and W , we consider the problem of deciding whether a smooth map f : V → W can be approximated by regular maps in the space of 𝒞 ∞ mappings from V to W in the 𝒞 ∞ topology. Our main result is a co
The first part of the chapter deals with general results about morphisms of algebraic varieties. Then these results are applied in the theory of algebraic groups. One of the main items of the chapter is the construction in 5.5 of the quotient of a linear algebraic group by a closed subgroup...