All Questions
Tagged with analytic-geometry real-algebraic-geometry
6
questions
9
votes
2
answers
1k
views
Embeddings and triangulations of real analytic varieties
This is a follow up question to my answer here How do you define the Euler Characteristic of a scheme?
A real analytic space is a ringed space locally isomorphic to $(X,O/I)$ where $X$ is the zero ...
- 23.2k
5
votes
1
answer
554
views
Polynomials (or analytic functions) vanishing on a real algebraic set
I have seen the following result stated several times in the literature, without proof:
Let $\mathbb{K}$ be $\mathbb{R}$ or $\mathbb{C}$, and assume $P\in\mathbb{K}[X_{1},\ldots,X_{n}]$ is an ...
- 3,731
5
votes
1
answer
305
views
Are continuous rational functions arc-analytic?
Let $X\subseteq\mathbb{R}^n$ be a smooth semi-algebraic set (for simplicity we can assume $X=B(0,r)$ is a small ball around the origin). A function $f:X\rightarrow \mathbb{R}$ is called a continuous ...
- 953
2
votes
3
answers
187
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How to tell if a second-order curve goes below the $x$ axis?
Suppose we have a second-order curve in general form:
(1) $a_{11}x^{2}+2a_{12}xy+a_{22}y^{2}+2a_{13}x+2a_{23}y+a_{33}=0$.
I'd like to know if there is a simple condition that ensures that the curve ...
- 6,832
2
votes
0
answers
62
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Unboundedness of number of solutions of intersection of bivariate polynomial with graph of function from an o-minimal structure
I am trying to understand a construction sketched in the paper by Gwozdziewicz, Kurdyka and Parusinski in the Proceedings of the AMS 1999 (paper here) and I'd like to request some help. The ...
2
votes
0
answers
98
views
Sheaves of functions on open semi-algebraic sets
Let $U\subsetneq\mathbb{R}^n$ be an open semi-algebraic set which is not Zariski open (the case I have in mind is that of an open ball $B(0,1)$). A function $f:U\rightarrow \mathbb{R}$ is called
(1) ...
- 953