By a theorem of Wahl, the canonically embedded curves which are hyperplane section of K3 surfaces are distinguished by the non-surjectivity of their Wahl map. In this paper we address the problem of distinguishing hyperplane sections of abelian surfaces. The somewhat surprising result is that the Wahl map of such curves is (tendentially) surjective, but their second Wahl map has corank at least...

A generalization of Lozanovskii's result is proved. Let E be k-dimensional sub-space of an n-dimensional Banach space with unconditional basis. 1 k ≤ e n k 2. This answers a question of V. Milman which appeared during a GAFA seminar talk about the hyperplane problem. We add logarithmical estimates concerning the hyperplane conjecture for proportional subspaces and quotients of Banach spaces wit...

State-of-the-art methods for clustering data drawn from a union of subspaces are based on sparse and low-rank representation theory. Existing results guaranteeing the correctness of such methods require the dimension of the subspaces to be small relative to the dimension of the ambient space. When this assumption is violated, as is, for example, in the case of hyperplanes, existing methods are ...

We study a tropical linear regression problem consisting in finding best approximation of set points by hyperplane. establish strong duality theorem, showing that the value this coincides with maximal radius Hilbert’s ball included polyhedron. also show is polynomial-time equivalent to mean payoff games. illustrate our results solving an inverse from auction theory. In setting, hyperplane repre...