Geodesic
Logarithmic bundles of multi-degree arrangements in $\Bbb P^n$
Documenta mathematica, Tome 20 (2015), pp. 507-529.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Let $ D = {D_{1}, \ldots, D_{\ell}} $ be a multi-degree arrangement with normal crossings on the complex projective space $ \{P}^n $, with degrees $ d_{1}, \ldots, d_{\ell} $; let $ \Omega_{\{P}^n}^1(\log D) $ be the logarithmic bundle attached to it. First we prove a Torelli type theorem when $ D $ has a sufficiently large number of components by recovering them as unstable smooth irreducible degree-$ d_{i} $ hypersurfaces of $ \Omega_{\{P}^n}^1(\log D) $. Then, when $ n = 2 $, by describing the moduli spaces containing $ \Omega_{\{P}^2}^1(\log D) $, we show that arrangements of a line and a conic, or of two lines and a conic, are not Torelli. Moreover we prove that the logarithmic bundle of three lines and a conic is related with the one of a cubic. Finally we analyze the conic-case.
Classification : 14J60, 14F05, 14C34, 14C20, 14N05
Keywords: multi-degree arrangement, hyperplane arrangement, logarithmic bundle, Torelli theorem 
@article{DOCMA_2015__20__a27,
     author = {Angelini, Elena},
     title = {Logarithmic bundles of multi-degree arrangements in $\Bbb P^n$},
     journal = {Documenta mathematica},
     pages = {507--529},
     publisher = {mathdoc},
     volume = {20},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2015__20__a27/}
}
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Angelini, Elena. Logarithmic bundles of multi-degree arrangements in $\Bbb P^n$. Documenta mathematica, Tome 20 (2015), pp. 507-529. http://geodesic.mathdoc.fr/item/DOCMA_2015__20__a27/