Scrolls and quartics.
La conjecture de “dualité étrange” de Le Potier donne un isomorphisme entre l’espace des sections du fibré déterminant sur deux espaces de modules différents de faisceaux semi-stables sur le plan projectif . Si on considère deux classes orthogonales dans l’algèbre de Grothendieck telles que est de rang strictement positif et est de rang zéro, on note et les espaces de modules de faisceaux semi-stables de classe , respectivement , sur . Il existe sur (resp. ) un fibré déterminant...
In this paper we compute the dimension of all the sth higher secant varieties of the Segre-Veronese embeddings Yd of the product P1 × P1 × P1 in the projective space PN via divisors of multidegree d = (a,b,c) (N = (a+1)(b+1)(c+1) - 1). We find that Yd has no deficient higher secant varieties, unless d = (2,2,2) and s = 7, or d = (2h,1,1) and s = 2h + 1, with defect 1 in both cases.
In this paper, we generalize the Gauduchon metrics on a compact complex manifold and define the functions on the space of its hermitian metrics.
A notion of positivity, called Seshadri ampleness, is introduced for a smooth curve in a polarized smooth projective -fold , whose motivation stems from some recent results concerning the gonality of space curves and the behaviour of stable bundles on under restriction to . This condition is stronger than the normality of the normal bundle and more general than being defined by a regular section of an ample rank- vector bundle. We then explore some of the properties of Seshadri-ample curves....