LetX be a smooth projective surface defined over C andH an ample divisor onX. LetMH(r; c1, c2) be the moduli space of stable sheaves of rank r whose Chern classes (c1, c2) ∈ H (X,Q)×H(X,Q) and MH(r; c1, c2) the Gieseker-Maruyama compactification of MH(r; c1, c2). When r = 2, these spaces are extensively studied by many authors. When r ≥ 3, Drezet and Le-Potier [D1],[D-L] investigated the struct...

An 1871 paper by Diekmann contains all the information needed to compute the integer singular homology for all classes of not ruled singular cubic surfaces. Three linearly independent quadrics in projective threespace deene a cubic Cremona transformation that associates to any point x the intersection of the polar planes of x with respect to the three quadrics. That intersection is a point y ex...

The paper introduces a new kind of special ruled surface. base each surface is taken to be one the Smarandache curves given curve according Frenet frame, and generator (ruling) chosen corresponding unit Darboux vector. characteristics these newly defined surfaces are investigated by means first second fundamental forms their curvatures. An example provided considering both helix Viviani’s curve.

It is well-known that there exists a bijection between the set of lines of the projective 3-dimensional space P3 and all real points of the so-called Plücker quadric Ψ. Moreover one can identify each point of the Plücker quadric’s ambient space with a linear complex of lines in P3. Within this paper we give an alternative interpretation for the points of P5 as lines of an Euclidean 4-space E4, ...