5
votes
1answer
188 views

Are there general position results in singular algebraic sets?

Let $X$ be a real algebraic set, and let $Y \subset X$ be its singular set. In this question I'll focus on the analytic topology, so we can just imagine that $X$ is the zero set, in $\mathbb{R}^n$, ...
6
votes
0answers
204 views

Real schubert calculus

Studying real enumerative questions I noticed, that the even-even Schubert varieties of the real Grassmannian $Gr:=Gr_{2k}(2n,\mathbb R)$ behave analogously to the complex case. I call a partition ...
0
votes
1answer
129 views

Real Pfaffian representations of real cubic surfaces

Consider the following classical construction (which is called Pfaffian representation as Sasha indicates): Let $ V^4\subset \Lambda^2 \mathbb R^6$ be a four-dimensional subspace of the space of ...
10
votes
1answer
557 views

Is the pairing between contours and functions perfect (modulo the kernel given by Stokes' theorem)?

Let $s: \mathbb C^n \to \mathbb C$ be a homogeneous degree-$d$ polynomial which is nonsingular (in the sense that the hypersurface it defines in $\mathbb{CP}^{n-1}$ is smooth; equivalently the ...
3
votes
4answers
487 views

Computation of the Euler characteristic of a specific real variety

I think computation of the Euler characteristic of a real variety is not a problem in theory. There are some nice papers like J.W. Bruce, Euler characteristics of real varieties. But suppose we ...
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 ...