When n satisfies an inequality which is almost best possible, we prove that the k-plane sections of every smooth, degree d, complex hypersurface in Pn dominate the moduli space of degree d hypersurfaces in Pk. As a corollary we prove that, for n sufficiently large, every smooth, degree d hypersurface in Pn satisfies a version of “rational simple connectedness”. 1. Statement of results In their ...

In this article, we consider hypersurfaces moving with normal velocity depending on the timespace coordinates and on the normal to the hypersurface. We naturally define a measure associated to this hypersurface. This measure is defined on a suitable space/unit normal/curvature configuration space. We show that, while the hypersurface stays smooth, then the measure is a solution to a linear tran...

In this paper we consider a variational problem for spacelike hypersurfaces in the (n + 1)-dimensional Lorentz-Minkowski space L, whose critical points are hypersurfaces supported in a spacelike hyperplane determined by two facts: the mean curvature is a linear function of the distance to and the hypersurface makes a constant angle with along its boundary. We prove that the hypersurface is rota...

We consider the dual billiard map with respect to a smooth strictly convex closed hypersurface in linear 2m-dimensional symplectic space and prove that it has at least 2m distinct 3-periodic orbits. AMS Classi cation 37J45, 70H12

We study the problem of optimizing a multiclass classifier based on its ROC hypersurface and a matrix describing the costs of each type of prediction error. For a binary classifier, it is straightforward to find an optimal operating point based on its ROC curve and the relative cost of true positive to false positive error. However, the corresponding multiclass problem (finding an optimal opera...

This article presents a performance measure, the actuation eficiency, which describes the imbalance between the end-effector accelerations achievable in different directions of non-redundant robotic manipulators. A key feature of the proposed measure is that in its development the unitam differences between linear and angular accelerations are treated in a physically meaningful manner. The memu...

From the degree zero part of the logarithmic vector fields along an algebraic hypersurface singularity we identify the maximal multihomogeneity of a defining equation in form of a maximal algebraic torus in the embedded automorphism group. We show that all such maximal tori are conjugate and in one–to–one correspondence to maximal tori in the linear jet of the embedded automorphism group. These...

Abstract. The hypersurface amoeba membership problem is the problem to decide whether for an input point λ ∈ R, the point λ is an element of the amoeba of the hypersurface generated by a multivariate complex Laurent polynomial c. We present an algorithm to solve this problem based on semidefinite programming and on Lasserre’s moment method for approximating the minimum of a real polynomial. The...

Our main object of study is X ⊂ P5F2 , where X is the degree 5 Fermat hypersurface, which we are looking at in P over F2. X is the zero locus {X 0 +X 1 + ...+X 5 = 0}. The question is, “what kind of rational curves lie on X?” Since F2 only has one invertible element, P(F2) = F 2 \ 0, which suggests that the Fermat quintic has the same zero locus as the linear hypersurface X0 + X1 + ... + X5 = 0...