We generalize the classical Terracini’s Lemma to higher order osculating spaces to secant varieties. As an application, we address with the so-called Horace method the case of the d-Veronese embedding of the projective 3-space. A.M.S. Math. Subject Classification (2000): 14N05.

The shape of a probability distribution is often summarized by the distribution’s skewness and kurtosis. Starting from a symmetric “parent” density f on the real line, we can modify its shape (i.e. introduce skewness and in-/decrease kurtosis) if f is appropriately weighted. In particular, every density w on the interval (0, 1) is a specific weighting function. Within this work, we follow up a ...

A generalization of the hyperbolic secant distribution which allows for both skewness and leptokurtosis was given by Morris (1982). Recently, Vaughan (2002) proposed another flexible generalization of the hyperbolic secant distribution which has a lot of nice properties but is not able to allow for skewness. For this reason, Fischer and Vaughan (2002) additionally introduced a skewness paramete...

We discuss the so-called secant conjecture in real algebraic geometry, and show that it follows from another interesting conjecture, about disconjugacy of vector spaces of real polynomials in one variable. AMS Class 2010: 14P99, 34C10, 26C10.

We study the algebraic varieties defined by the conditional independence statements of Bayesian networks. A complete algebraic classification is given for Bayesian networks on at most five random variables. Hidden variables are related to the geometry of higher secant varieties.

We use the geometry of the secant variety to an embedded smooth curve to prove some vanishing and regularity theorems for powers of ideal sheaves. 1991 Subject Classification: Primary 14F17; Secondary 14H60,14N05

Let X be a semi-stable arithmetic surface over the spectrum S of the ring of integers in a number field K. We assume that the generic fiber XK is geometrically irreducible and has positive genus. Consider a line bundle L on X , which is non-negative on every vertical fiber and equipped with an admissible metric (in the sense of Arakelov [A]) of positive curvature. In [S] we have shown that any ...

Let C be a curve in P3 over an algebraically closed field of characteristic zero. We assume that C is nonsingular and contains no plane component except possibly an irreducible conic. In [GP] one defines closed r-secant varieties to C, r £ N. These varieties are embedded in G, the Grassmannian of lines in P3. Denote by T the 3-secant variety (curve), and assume that the set of 4-secants is fini...