MOTIVES AND THE HODGE CONJECTURE FOR MODULI SPACES OF PAIRS

作者：Munoz Vicente^*; Oliveira Andre G; Sanchez Jonathan

来源：Asian Journal of Mathematics, 2015, 19(2): 281-305.

DOI：10.4310/ajm.2015.v19.n2.a5

• Moduli space
• complex curve
• vector bundle
• motives
• Hodge conjecture

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.

• 出版日期2015-4