Schwartz Functions on Real Algebraic Varieties
نویسندگان
چکیده
منابع مشابه
Toric completions and bounded functions on real algebraic varieties
Given a semialgebraic set S, we study compactifications of S that arise from embeddings into complete toric varieties. This makes it possible to describe the asymptotic growth of polynomial functions on S in terms of combinatorial data. We extend our earlier work in [10] to compute the ring of bounded functions in this setting and discuss applications to positive polynomials and the moment prob...
متن کاملSums of Squares of Regular Functions on Real Algebraic Varieties
Let V be an affine algebraic variety over R (or any other real closed field R). We ask when it is true that every positive semidefinite (psd) polynomial function on V is a sum of squares (sos). We show that for dimV ≥ 3 the answer is always negative if V has a real point. Also, if V is a smooth non-rational curve all of whose points at infinity are real, the answer is again negative. The same h...
متن کاملPositivity Functions for Curves on Algebraic Varieties
This is the second part of our work on Zariski decomposition structures, where we compare two different volume type functions for curve classes. The first function is the polar transform of the volume for ample divisor classes. The second function captures the asymptotic geometry of curves analogously to the volume function for divisors. We prove that the two functions coincide, generalizing Za...
متن کاملThe Weight Filtration for Real Algebraic Varieties
Using the work of Guillén and Navarro Aznar we associate to each real algebraic variety a filtered chain complex, the weight complex, which is well-defined up to filtered quasi-isomorphism, and which induces on Borel-Moore homology with Z2 coefficients an analog of the weight filtration for complex algebraic varieties. The weight complex can be represented by a geometrically defined filtration ...
متن کاملReal Algebraic Varieties with Prescribed Tangent Cones
The definition of the tangent cone C(V, p) to an algebraic variety V at a point p was given by Whitney more than 40 years ago as one of the tools to get information about the geometric shape of a variety near a singular point. While the complex case has been widely and successfully studied, including from a computational point of view, only recently have some first attempts been made to elucida...
متن کاملذخیره 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: Canadian Journal of Mathematics
سال: 2018
ISSN: 0008-414X,1496-4279
DOI: 10.4153/cjm-2017-042-6