The Orlik-terao Algebra and 2-formality
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چکیده
The Orlik-Solomon algebra is the cohomology ring of the complement of a hyperplane arrangement A ⊆ Cn; it is the quotient of an exterior algebra Λ(V ) on |A| generators. In [9], Orlik and Terao introduced a commutative analog Sym(V ∗)/I of the Orlik-Solomon algebra to answer a question of Aomoto and showed the Hilbert series depends only on the intersection lattice L(A). In [6], Falk and Randell define the property of 2-formality; in this note we study the relation between 2-formality and the Orlik-Terao algebra. Our main result is a necessary and sufficient condition for 2formality in terms of the quadratic component I2 of the Orlik-Terao ideal I. The key is that 2-formality is determined by the tangent space Tp(V (I2)) at a generic point p.
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تاریخ انتشار 2009