The Module of Logarithmic p-forms of a Locally Free Arrangement
| dc.creator | Mustata, Mircea | |
| dc.creator | Schenck, Hal | |
| dc.date | 2000-01-30 | |
| dc.date.accessioned | 2026-07-07T04:33:30Z | |
| dc.date.available | 2026-07-07T04:33:30Z | |
| dc.description | For an essential, central hyperplane arrangement A in V=k^{n+1}, we show that Ω^1(A) (the module of logarithmic one forms with poles along A) gives rise to a locally free sheaf on P^n if and only if for all X in L_A with rank X<dim V, the module Ω^1(A_X) is free. Our main result is that in this case the Poicare polynomial of A is essentially the Chern polynomial. The proof is based on a result of Solomon and Terao and on a formula we give for the Chern polynomial of a bundle E on P^n in terms of the Hilbert series of \oplus_m H^0(\wedge^iE(m)). If Ω^1(A)has projective dimension one and is locally free, we give a minimal free resolution for Ω^p, and show that \wedge^p(Ω^1(A))\isoΩ^p(A), generalizing results of Rose and Terao on generic arrangements. | |
| dc.description | LaTeX, 17 pages | |
| dc.identifier | https://arxiv.org/abs/math/0001177 | |
| dc.identifier | http://arxiv.org/abs/math/0001177 | |
| dc.identifier | J. Algebra 241 (2001), no. 2, 699-719. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/58597 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14J60 (Primary); 14Q10 (Secondary) | |
| dc.title | The Module of Logarithmic p-forms of a Locally Free Arrangement | |
| dc.type | text |