We study curves with linear series that are exceptional with regard to their secant planes. Working in the framework of an extension of Brill-Noether theory to pairs of linear series, we prove that a general curve of genus g has no exceptional secant planes, in a very precise sense. We also address the problem of computing the number of linear series with exceptional secant planes in a one-para...

We shall introduce and study quadratic entry locus varieties, a class of projective algebraic varieties whose extrinsic and intrinsic geometry is very rich. Let us recall that, for an irreducible non-degenerate variety X ⊂ P of dimension n ≥ 1, the secant defect of X , denoted by δ(X), is the difference between the expected dimension and the effective dimension of the secant variety SX ⊆ P of X...

We shall introduce and study quadratic entry locus varieties, a class of projective algebraic varieties whose extrinsic and intrinsic geometry is very rich. Let us recall that, for an irreducible non-degenerate variety X ⊂ P of dimension n ≥ 1, the secant defect of X , denoted by δ(X), is the difference between the expected dimension and the effective dimension of the secant variety SX ⊆ P of X...

the assumptions considered in developing the saint-venant equations limit their application in many practical situations. the modified boussinesq equation was presented to overcome the limitation imposed by saint-venant equation due to the presence of non-hydrostatic pressure distribution and steep slope. in this paper a computational model was developed for solving the modified and the traditi...

Let X ⊆ PN be a non-degenerate projective variety of dimension d. Then the sth secant variety of X, denoted σs(X), is the Zariski closure of the union of linear spans of s-tuples of points lying on X. The study of secant varieties has a long history. The interest in this subject goes back to the Italian school at the turn of the 20th century. This topic has received renewed interest over the pa...

We show that the secant varieties of rank three compact Hermitian symmetric spaces in their minimal homogeneous embeddings are normal, with rational singularities. We show that their ideals are generated in degree three with one exception, the secant variety of the 21-dimensional spinor variety in P, whose ideal is generated in degree four. We also discuss the coordinate ring of secant varietie...

For a variety X of dimension n in Pr, r n(k + 1) + k, the kth secant order of X is the number μk(X) of (k + 1)-secant k-spaces passing through a general point of the kth secant variety. We show that, if r > n(k + 1) + k, then μk(X) = 1 unless X is k-weakly defective. Furthermore we give a complete classification of surfaces X ⊂ Pr, r > 3k + 2, for which μk(X) > 1.