The module of logarithmic p-forms of a locally free arrangement
By M. Mustaţă, H. Schenck. 2000
61 citations recorded by the source corpus.
For an essential, central hyperplane arrangement A ⊆ V ≃ k n+1 we show that 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 ∈ LA with rank X < dim V , the module 1 (AX) is free. Our main result says that in this case �(A,t) is essentially the Chern polynomial. The proof is based on a result of Solomon-Terao [16] and a formula we give for the Chern polynomial of a bundle E on P n in terms of the Hilbert series of ⊕m2ZH 0 (P n , ∧ i E(m)). If 1 (A) has projective dimension one and is locally free, we give a minimal
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/da34b4a889b74044fa74a3212c2ac54fde7fa9bd
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In Geometry and Topology
- Max Wakefield
- Takuro Abe
- Stefan O. Tohaneanu
- H. Schenck
- Masahiko Yoshinaga
- Alexandru Dimca
- Nicholas Proudfoot
- David E. Speyer
In Mathematical Physics
- Takuro Abe
- Max Wakefield
- H. Schenck
- Hiroaki Terao
- Masahiko Yoshinaga
- Nicholas Proudfoot
- David E. Speyer
Citations in the corpus
- THE CHARACTERISTIC POLYNOMIAL OF A MULTIARRANGEMENT (2006, background): “The next definition is a generalization of the ideas of locally free arrangements in [3] and [16].”
- Freeness of conic-line arrangements in P2 (2009, background): “1 of [4] gives the desired bound on depth for the modules of derivations, which concludes the proof.”
- Elementary modifications and line configurations in ℙ2 (2003, background): “Since the sheaf D is reflexive, it corresponds to a bundle on P(2) and ([12])”