Elementary modifications and line configurations in ℙ2
By H. Schenck. 2003
68 citations recorded by the source corpus.
AbstractAssociated to a projective arrangement of hyperplanes ${\mathcal A}$ ⊆ ℙn is the module D$({\mathcal A})$, which consists of derivations tangent to ${\mathcal A}$. We study D$({\mathcal A})$ when ${\mathcal A}$ is a configuration of lines in ℙ2. In this setting, we relate the deletion/restriction construction used in the study of hyperplane arrangements to elementary modifications of bundles. This allows us to obtain bounds on the Castelnuovo-Mumford regularity of D$({\mathcal A})$. We also give simple combinatorial conditions for the associated bundle to be stable, and describe its jump lines. These regularity bounds and stability considerations impose constraints on Terao’s conjecture.
Subfields: Algebra and Number Theory, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/9827190f5fb2a42db9bd4d8013db19b792cf6808
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In Algebra and Number Theory
In Geometry and Topology
Citations in the corpus
- Freeness versus maximal global Tjurina number for plane curves (2015, background): “Terao has conjectured that if A and A′ are hyperplane arrangements in P with isomorphic intersection lattices L(A) = L(A′), and if A is free, then A′ is also free, see for details [12], [17] as well as [14] for the case n = 2.”