A. Khovanskii

collaborators

3 papers

math.DG2002

L-convex-concave sets in real projective space and L-duality

A. Khovanskii, D. Novikov

We define a class of L-convex-concave subsets of $R P^{n}$ , where L is a projective subspace of dimension l in $R P^{n}$ . These are sets whose sections by any (l+1)-dimension…

math.DG2002

On affine hypersurfaces with everywhere nondegenerate Second Quadratic Form

A. Khovanskii, D. Novikov

Consider a closed connected hypersurface in $R^{n}$ with constant signature (k,l) of the second quadratic form, and approaching a quadratic cone at infinity. This hypersurfa…

math.DG2002

Convex-concave body in $R P^{3}$ contains a line

A. Khovanskii, D. Novikov

We define a class of $L$ -convex-concave subsets of $R P^{3}$ , where $L$ is a projective line in $R P^{3}$ . These are sets whose sections by any plane containing $L$ are…

L-convex-concave sets in real projective space and L-duality

On affine hypersurfaces with everywhere nondegenerate Second Quadratic Form

Convex-concave body in RP3 contains a line

Convex-concave body in $R P^{3}$ contains a line