Bézoutians and injectivity of polynomial maps

نویسندگان

چکیده

We prove that an endomorphism $f$ of affine space is injective on rational points if its B\'ezoutian constant. Similarly, at a given point reduced also show the Jacobian determinant invertible, then and only

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Continuity and Injectivity of Optimal Maps

Figalli–Kim–McCann proved in [14] the continuity and injectivity of optimal maps under the assumption (B3) of nonnegative cross-curvature. In the recent [15, 16], they extend their results to the assumption (A3w) of Trudinger-Wang [34], and they prove, moreover, the Hölder continuity of these maps. We give here an alternative and independent proof of the extension to (A3w) of the continuity and...

متن کامل

Approximate Maps Characterizing Injectivity and Surjectivity of Maps

In the theory of inverse systems, in order to study the properties of a space X or a map f : X → Y between spaces, one expands X to an inverse system X or expands f to a map f : X → Y between the inverse systems, and then work on X or f . In this paper, we define approximate injectivity (resp., surjectivity) for approximate maps, and show that a map f : X → Y between compact metric spaces is in...

متن کامل

Hölder continuity and injectivity of optimal maps∗

Consider transportation of one distribution of mass onto another, chosen to optimize the total expected cost, where cost per unit mass transported from x to y is given by a smooth function c(x, y). If the source density f(x) is bounded away from zero and infinity in an open region U ′ ⊂ R, and the target density f−(y) is bounded away from zero and infinity on its support V ⊂ R, which is strongl...

متن کامل

Sign Conditions for Injectivity of Generalized Polynomial Maps with Applications to Chemical Reaction Networks and Real Algebraic Geometry

We give necessary and sufficient conditions in terms of sign vectors for the injectivity of families of polynomial maps with arbitrary real exponents defined on the positive orthant. Our work relates and extends existing injectivity conditions expressed in terms of Jacobian matrices and determinants. In the context of chemical reaction networks with power-law kinetics, our results can be used t...

متن کامل

One-one Polynomial Maps

It is a fundamental fact about simultaneous linear equations that uniqueness implies existence in the sense that if the »X» system MX= Y has, for each Y, at most one solution X, then, for each Y, the equation actually has a solution. Our purpose is to show that this situation persists for certain "nonlinear equations" as well, namely that, restricting everything to the reals, if Pi, P2 are poly...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Journal of Pure and Applied Algebra

سال: 2023

ISSN: ['1873-1376', '0022-4049']

DOI: https://doi.org/10.1016/j.jpaa.2022.107298