Freeness of hyperplane arrangements and related topics

By Masahiko Yoshinaga. 2012

81 citations recorded by the source corpus.

This is the expanded notes of the lecture by the author in "Arrangements in Pyrenees", June 2012. We are discussing relations of freeness and splitting problems of vector bundles, several techniques proving freeness of hyperplane arrangements, K. Saito's theory of primitive derivations for Coxeter arrangements, their application to combinatorial problems and related conjectures.

Subfields: Applied Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/98cd916c059f1b060345b1465e853d27dd419d48

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In Applied Mathematics

1. Takuro Abe
2. Alexandru Dimca
3. E. Sernesi

In Discrete Mathematics and Combinatorics

1. E. Sernesi
2. Takuro Abe
3. Alexandru Dimca

In Geometry and Topology

1. Alexandru Dimca
2. E. Sernesi
3. Takuro Abe
4. F. Catanese

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.”
• Plus-one Generated and Next to Free Arrangements of Hyperplanes (2018, background): “A is locally free if and only if the sheaf D̃H(A) is a vector bundle on P = P(V ) = Proj(S) for any (equivalently, some) H ∈ A (see [23], Proposition 1.”
• Syzygies and logarithmic vector fields along plane curves (2014, background): “For more on this equivalence we refer to [30] and the references there.”