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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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Official URL: http://intlpress.com/site/pub/pages/journals/items/ajm/content/vols/0019/0002/a005/body.html

## Abstract

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 |
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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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