Motives and the Hodge conjecture for moduli spaces of pairs



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Muñoz, Vicente and Oliveira, André G. and Sánchez Hernández, Jonathan (2015) Motives and the Hodge conjecture for moduli spaces of pairs. Asian journal of mathematics, 19 (2). pp. 281-306. ISSN 1093-6106

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Let C be a smooth projective curve of genus g >= 2 over C. Fix n >= 1, d is an element of Z. A pair (E, phi) over C consists of an algebraic vector bundle E of rank n and degree d over C and a section phi is an element of H-0(E). There is a concept of stability for pairs which depends on a real parameter tau. Let M-tau (n, d) be the moduli space of tau-polystable pairs of rank n and degree d over C. We prove that for a generic curve C, the moduli space M-tau (n, d) satisfies the Hodge Conjecture for n <= 4. For obtaining this, we prove first that M-tau (n, d) is motivated by C.

Item Type:Article
Uncontrolled Keywords:Moduli space; complex curve; vector bundle; motives; Hodge conjecture
Subjects:Sciences > Mathematics > Geometry
Sciences > Mathematics > Topology
ID Code:31324
Deposited On:07 Jul 2015 08:48
Last Modified:12 Dec 2018 15:12

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