A concrete example of symplectic duality among K-3 surfaces

An explicit example of symplectic duality among two particular K-3 surfaces is given. The example was considered by Iliev and Ranestad. Here, by using projective and computer algebra methods, it is proved that the two surfaces are in fact dominated by a 3-fold

Reducible Veronese surfaces

We describe all degree n+3 non degenerate surfaces in P^(n+4), n 651, connected in codimension 1, which may be isomorphically projected into P^4. There are three of them. One is a suitable union of n+3 planes (for all n 651); it was discovered by Floystad. The otheer two are unions of a smooth quadric and two planes (only for n=1)

General position of points on a rational ruled surface

In this note we introduce a definition of general position for distinct points on a rational ruled surface and we discuss some related properties having in mind very ampleness criteria for rank 2 vector bundles

An explicit construction of ruled surfaces

The main goal of this paper is to give a general algorithm to compute, via computer-algebra systems, an explicit set of generators of the ideals of the projective embeddings of ruled surfaces, i.e. projectivizations of rank two vector bundles over curves, such that the fibers are embedded as smooth rational curves. There are two different applications of our algorithm. Firstly, given a very ample linear system on an abstract ruled Surface, our algorithm allows computing the ideal of the embedded surface, all the syzygies, and all the algebraic invariants which are computable from its ideal as, for instance, the k-regularity. Secondly, it is possible to prove the existence of new embeddings of ruled surfaces, The method can be implemented over any computer-algebra system able to deal with commutative algebra and Grobner-basis computations. An implementation of our algorithms for the computer-algebra system Macaulay2 (cf. [Daniel R. Grayson, Michael E. Stillman, Macaulay 2, a software system for research in algebraic geometry, 1993. Available at http://www.math.uiuc.edu/Macaulay2/]) and explicit examples are enclosed

J-embeddable reducible surfaces

We classify J-embeddable surfaces, i.e. surfaces whose secant varieties have dimension at most 4, when the surfaces have two component at most

Projectable Veronese varieties

Let X be a non degenerate, reduced, reducible algebraic variety embedded in a"(TM) (N) , of pure dimension ma parts per thousand yen3. X is said to be an x-projectable Veronese variety if, assuming Na parts per thousand yenm+x+1, X is of minimal degree, connected in codimension 1 and isomorphically projectable into a linear space of dimension m+x

Corrigenda to "Reducible Veronese surfaces"

We correct the definition and the list of all reducible Veronese surfaces in our previous paper "Reducible Veronese surfaces", Adv. Geom. 10 (2010), 719-735

Special birational transformations of projective spaces

Extending some results of Crauder and Katz and Ein and Sheperd-Barron on special Cremona transformations, we study birational transformations of P^r onto a prima Fano manifold such that the base locus X in P^r is smooth, irreducible and reduced. The main results are a complete classification when X has either dimension 1 and 2 or codimension 2. Partial results are also obtained when X has dimension 3

Camera re-calibration after zooming based on sets of conics

We describe a method to compute the internal parameters (focal and principal points) of a camera with known position and orientation, based on the observation of two or more conics on a known plane. The conics can even be degenerate (e.g. pairs of lines). The proposed method can be used to re-estimate the internal parameters of a fully calibrated camera after zooming to a new, unknown, focal length. It also allows estimating the internal parameters when a second, fully calibrated camera observes the same conics. The parameters estimated through the proposed method are coherent with the output of more traditional procedures that require a higher number of calibration images. A deep analysis of the geometrical configurations that influence the proposed method is also reported