Unitary local systems, multiplier ideals, and polynomial periodicity of Hodge numbers

By Nero Budur. 2006

58 citations recorded by the source corpus.

Abstract The space of unitary local systems of rank one on the complement of an arbitrary divisor in a complex projective algebraic variety can be described in terms of parabolic line bundles. We show that multiplier ideals provide natural stratifications of this space. We prove a structure theorem for these stratifications in terms of complex tori and convex rational polytopes, generalizing to the quasi-projective case results of Green–Lazarsfeld and Simpson. As an application we show the polynomial periodicity of Hodge numbers h q , 0 of congruence covers in any dimension, generalizing results of E. Hironaka and Sakuma. We extend the structure theorem and polynomial periodicity to the setting of cohomology of unitary local systems. In particular, we obtain a generalization of the polynomial periodicity of Betti numbers of unbranched congruence covers due to Sarnak–Adams. We derive a geometric characterization of finite abelian covers, which recovers the classic one and the one of Pardini. We use this, for example, to prove a conjecture of Libgober about Hodge numbers of abelian covers.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/4db878f18fec0de8eec87c85af72e2d26cfde9fb

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In Algebra and Number Theory

1. J. Cogolludo-Agustín
2. Daniel Matei
3. Nero Budur
4. Enrique Artal Bartolo

In Geometry and Topology

1. J. Cogolludo-Agustín
2. Daniel Matei
3. Nero Budur
4. Enrique Artal Bartolo
5. Morihiko Saito

In Mathematical Physics

1. J. Cogolludo-Agustín
2. Daniel Matei
3. Nero Budur
4. Enrique Artal Bartolo
5. Morihiko Saito

Citations in the corpus

• Characteristic varieties of quasi-projective manifolds and orbifolds (2010, background): “(resp. Campana [11]). In the noncompact case it was proved by Libgober [36] for quasi-projective manifolds X with b1(X¯) = 0. Dimca in [26] pointed out that this fact may be deduced from Budur’s work [10] for general quasi-projective varieties. This can be done with a big amount of work, however, we”
• Bernstein-Sato ideals and local systems (2012, background): “ogy jump loci, characteristic variety, Sabbah specialization, Alexander module, Milnor fiber, Monodromy Conjecture, hyperplane arrangements. 1 2 NEROBUDUR [19, 20], Arapura [1, 2], Simpson [42], Budur [9], Libgober [27], Dimca-PapadimaSuciu [17], Popa-Schnell [37], Dimca-Papadima [16]. The union of t”