Let D = {D_1, . . . ,D_ℓ} be a multi-degree arrangement with normal crossings on the complex projective space P^n, with degrees d_1, . . . , d_ℓ; let consider 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 the logarithmic bundle. Then, when n = 2, by describing the moduli spaces containing the logarithmic bundle, 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.

### Logarithmic bundles of multi-degree arrangements in P^n

#### Abstract

Let D = {D_1, . . . ,D_ℓ} be a multi-degree arrangement with normal crossings on the complex projective space P^n, with degrees d_1, . . . , d_ℓ; let consider 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 the logarithmic bundle. Then, when n = 2, by describing the moduli spaces containing the logarithmic bundle, 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.
##### Scheda breve Scheda completa Scheda completa (DC)
2015
Angelini, Elena
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in SFERA sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11392/2336177`
##### Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

• ND
• 1
• 1