### Chern classes of fibered products of surfaces.

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Continuing our work on the fundamental groups of conic-line arrangements (Amram et al., 2003), we obtain presentations of fundamental groups of the complements of three families of quadric arrangements in P. The first arrangement is a union of n conics, which are tangent to each other at two common points. The second arrangement is composed of n quadrics which are tangent to each other at one common point. The third arrangement is composed of n quadrics, n-1 of them are tangent to the n-th one and...

The classical Segre theory gives a necessary and sufficient condition for a plane curve to be a branch curve of a (generic) projection of a smooth surface in ${\mathbb{P}}^{3}$. We generalize this result for smooth surfaces in a projective space of any dimension in the following way: given two plane curves, $B$ and $E$, we give a necessary and sufficient condition for $B$ to be the branch curve of a surface $X$ in ${\mathbb{P}}^{N}$ and $E$ to be the image of the double curve of a ${\mathbb{P}}^{3}$-model of $X$. In the classical Segre theory, a plane curve...

We study some geometric configurations related to projections of an irreducible algebraic curve embedded in $\u2102{\mathbb{P}}^{3}$ onto embedded projective planes. These configurations are motivated by applications to static and dynamic computational vision. More precisely, we study how an irreducible closed algebraic curve $X$ embedded in $\u2102{\mathbb{P}}^{3}$, of degree $d$ and genus $g$, can be recovered using its projections from points onto embedded projective planes. The embeddings are unknown. The only input is the defining equation of...

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