Geodesic
On ramified covers of the projective plane II: Generalizing Segre’s theory
Journal of the European Mathematical Society, Tome 14 (2012) no. 3, pp. 971-996

Voir la notice de l'article provenant de la source EMS Press

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 P3. 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 PN and E to be the image of the double curve of a P3-model of X. In the classical Segre theory, a plane curve B is a branch curve of a smooth surface in P3 iff its 0-cycle of singularities is special with respect to a linear system of plane curves of particular degree. Here we prove that B is a branch curve of a surface in PN iff (part of) the cycle of singularities of the union of B and E is special with respect to the linear system of plane curves of a particular low degree. In particular, given just a curve B, we provide some necessary conditions for B to be a branch curve of a smooth surface in PN.
DOI : 10.4171/jems/324
Classification : 14-XX, 00-XX
Keywords: branch curves, adjoint curves, ramified covers 
@article{JEMS_2012_14_3_a11,
     author = {Michael Friedman and Rebecca Lehman and Maxim Leyenson and Mina Teicher},
     title = {On ramified covers of the projective plane {II:} {Generalizing} {Segre{\textquoteright}s} theory},
     journal = {Journal of the European Mathematical Society},
     pages = {971--996},
     publisher = {mathdoc},
     volume = {14},
     number = {3},
     year = {2012},
     doi = {10.4171/jems/324},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/324/}
}
TY  - JOUR
AU  - Michael Friedman
AU  - Rebecca Lehman
AU  - Maxim Leyenson
AU  - Mina Teicher
TI  - On ramified covers of the projective plane II: Generalizing Segre’s theory
JO  - Journal of the European Mathematical Society
PY  - 2012
SP  - 971
EP  - 996
VL  - 14
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4171/jems/324/
DO  - 10.4171/jems/324
ID  - JEMS_2012_14_3_a11
ER  - 
%0 Journal Article
%A Michael Friedman
%A Rebecca Lehman
%A Maxim Leyenson
%A Mina Teicher
%T On ramified covers of the projective plane II: Generalizing Segre’s theory
%J Journal of the European Mathematical Society
%D 2012
%P 971-996
%V 14
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4171/jems/324/
%R 10.4171/jems/324
%F JEMS_2012_14_3_a11
Michael Friedman; Rebecca Lehman; Maxim Leyenson; Mina Teicher. On ramified covers of the projective plane II: Generalizing Segre’s theory. Journal of the European Mathematical Society, Tome 14 (2012) no. 3, pp. 971-996. doi: 10.4171/jems/324

Cité par Sources :