4
votes
2answers
458 views

Real vs complex surfaces

Hi! My background is in (complex) algebraic geometry. For the first time I'm considering varieties defined over $\mathbb{R}$ and I have some very basic questions about these. In particular I'm trying ...
1
vote
1answer
326 views

Number of connected components of complement to a reducible real algebraic hypersurface.[EDITED]

Let $X_1,\ldots X_k$ be irreducible(may be singular) affine real algebraic hypersurfaces in $R^n$ with $x_1,\ldots, x_k$ connected components, respectively. Let $G_1,\ldots, G_l$ be their ...
6
votes
2answers
528 views

Maximal number of connected components of complement to an affine plane real algebraic curve

Let $X$ be a (singular, reducible) affine plane real algebraic curve of degree $d$. How we can estimate maximal number of connected components of it's complement in $R^2$ in terms of degree?