Resonance varieties via blowups of P^2 and scrolls

Details Resonance varieties via blowups of P^2 and scrolls Resonance varieties via blowups of P^2 and scrolls

2010-12-04

arxiv.org/abs/1012.0931v1

International Mathematics Research Notices, 20, (2011) 4756-4778. o

Mathematics

Algebraic Geometry

15 pages, 4 figures

Scientific paper

Conjectures of Suciu relate the fundamental group of the complement M = C^n\A of a hyperplane arrangement A to the first resonance variety of H^*(M,Z). We describe a connection between the first resonance variety and the Orlik-Terao algebra C(A) of the arrangement. In particular, we show that non-local components of R^1(A) give rise to determinantal syzygies of C(A). As a result, Proj(C(A)) lies on a scroll, placing geometric constraints on R^1(A). The key observation is that C(A) is the homogeneous coordinate ring associated to a nef but not ample divisor on the blowup of P^2 at the singular points of A.

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