Generic splitting-type conjecture for logarithmic bundles of line arrangements

Let A{\mathcal A} and B{\mathcal B} be line arrangements with isomorphic intersection lattices

L(A)L(B).L({\mathcal A})\cong L({\mathcal B}).

Let E(A)E({\mathcal A}) and E(B)E({\mathcal B}) be the associated rank 22 vector bundles on P2\mathbb{P}^2. For a generic line LL, the restriction of each bundle splits as a direct sum of two line bundles; this pair is its generic splitting type. Generic splitting-type conjecture. The bundles E(A)E({\mathcal A}) and E(B)E({\mathcal B}) have the same generic splitting type. Over C\mathbb{C}, the source presents this as an equivalent geometric form of the stronger Terao conjecture. The supplied excerpt does not establish a resolution.

Sources & referencesView supporting material

Primary source

Takuro Abe, Alexandru Dimca and Gabriel Sticlaru, “Addition-deletion results for the minimal degree of logarithmic derivations of arrangements”, arXiv:1908.06885 (2019).

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