During the last twenty years algebraic geometry has experienced a remarkable shift from
development of abstract theories to investigation of concrete properties of projective …

A $ d $-dimensional {\it framework} is a graph and a map from its vertices to~ ${\Bbb E}^ d $.
Such a framework is {\it globally rigid} if it is the only framework in ${\Bbb E}^ d $ with the …

In this chapter, we develop the theme of estimating dimensions of joins and sets of
tangencies, often under assumptions of connectedness, using results from Chapter 3. In …

A projective variety $ X $ is '$ k $-weakly defective'when its intersection with a general $(k+
1) $-tangent hyperplane has no isolated singularities at the $ k+ 1$ points of tangency. If $ X …

Projective duality is a very classical notion naturally arising in various areas of mathematics,
such as algebraic and differential geometry, combinatorics, topology, analytical mechanics …

For several centuries, various reincarnations of projective duality have inspired research in
algebraic and differential geometry, classical mechanics, invariant theory, combinatorics …

Abstract Let X⊂ P be an irreducible closed subvariety of projective space. The k th higher
secant variety of X, denoted X k, is the closure of the union of all linear spaces spanned by k …

1. Introduction and conventions. One way to study geometric properties of a variety Xn c (I]
Pn+ a is by studyingcoarse geometric properties of auxiliary varieties one constructs from X …

A d-dimensional framework is a pair vertices, then the d-dimensional generic rigidity matroid
of G is connected. Finally, we provide new families of fully reconstructible graphs and use …

Over an algebraically closed field, the $\textit {double point interpolation} $ problem asks for
the vector space dimension of the projective hypersurfaces of degree $ d $ singular at a …