Geodesic
Logarithmic bundles of multi-degree arrangements in $\Bbb P^n$
Documenta mathematica, Tome 20 (2015), pp. 507-529
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Let D=D1​,...,Dl​ be a multi-degree arrangement with normal crossings on the complex projective space Pn, with degrees d1​,...,dl​; let ΩPn1​(logD) 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-di​ hypersurfaces of ΩPn1​(logD). Then, when n=2, by describing the moduli spaces containing ΩP21​(logD), 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.
DOI : 10.4171/dm/497
Classification : 14C20, 14C34, 14J60, 14N05
Mots-clés : multi-degree arrangement, hyperplane arrangement, logarithmic bundle, Torelli theorem 
@article{10_4171_dm_497,
     author = {Elena Angelini},
     title = {Logarithmic bundles of multi-degree arrangements in $\Bbb P^n$},
     journal = {Documenta mathematica},
     pages = {507--529},
     year = {2015},
     volume = {20},
     doi = {10.4171/dm/497},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/497/}
}
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Elena Angelini. Logarithmic bundles of multi-degree arrangements in $\Bbb P^n$. Documenta mathematica, Tome 20 (2015), pp. 507-529. doi: 10.4171/dm/497

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