About restricting 2-bundles on IP3 to planes.
In this article we describe our experiences with a parallel Singular implementation of the signature of a surface singularity defined by z N + g(x; y) = 0.
We express the Euler-Poincaré characteristic of a semi-algebraic set, which is the intersection of a non-singular complete intersection with two polynomial inequalities, in terms of the signatures of appropriate bilinear symmetric forms.
In this paper we show that on a general hypersurface of degree r = 3,4,5,6 in P5 a rank 2 vector bundle ε splits if and only if h1ε(n) = h2ε(n) = 0 for all n ∈ Z. Similar results for r = 1,2 were obtained in [15], [16] and [2].
We review some facts about rank two arithmetically Cohen-Macaulay bundles on quintic threefolds. In particular, we separate them into seventeen natural classes, only fourteen of which can appear on a general quintic. We discuss some enumerative problems arising from these.
Let C be a smooth integral projective curve admitting two pencils ga1 and gb1 such that ga1 + gb1 is birational. We give conditions in order that the complete linear system |sga1 + rgb1| be normally generated or very ample.