Picard Numbers of Surfaces in 3-Dimensional Weighted Projective Spaces.
Let C be a smooth non-degenerate integral curve of degree d and genus g in over an algebraically closed field of characteristic zero. For each point P in let be the linear system on C induced by the hyperplanes through P. By one maps C onto a plane curve , such a map can be seen as a projection of C from P. If P is not the vertex of a cone of bisecant lines, then will have only finitely many singular points; or to put it slightly different: The secant scheme parametrizing divisors in...
We classify all smooth projective varieties of degree 4 and describe their syzygies.