Brauer Group of Moduli Spaces of Pairs

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

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“…It has fiber P Hom(L e , L 1 ). The same argument as in the proof of Proposition 3.2 in [7] shows that the Brauer class…”

Section: Now We Move To the Casementioning

confidence: 53%

“…It has fiber P Hom(L e , L 1 ). The same argument as in the proof of Proposition 3.2 in [7] shows that the Brauer class cl(U m ) ∈ Br(M s (n 1 , d 1 )) satisfies cl(U m ) = ± cl(X + T ′ ). (6.1)…”

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confidence: 70%

Motives and the Hodge conjecture for moduli spaces of pairs

Muñoz

Oliveira

Sánchez

2015

Asian Journal of Mathematics

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“…In [15], a Torelli type theorem for the moduli spaces M τ (r, Λ) is proved; this amounts to the following: the algebraic structure of the moduli space allows to recover the complex structure of X. We also mention that in [4], the authors compute the Brauer group of these moduli spaces.…”

Section: Introductionmentioning

confidence: 99%

Rationality of the Moduli Space of Stable Pairs over a Complex Curve

Biswas

Logares

Muñoz

2012

Springer Optimization and Its Applications

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Abstract. Let X be a smooth complex projective curve of genus g ≥ 2. A pair on X is formed by a vector bundle E → X and a global non-zero section φ ∈ H 0 (E). There is a concept of stability for pairs depending on a real parameter τ , giving rise to moduli spaces M τ (r, Λ) of τ -stable pairs of rank r and fixed determinant Λ. In this paper we prove that the moduli spaces M τ (r, Λ) are in many cases rational.Dedicated to the 60th Anniversary of Themistocles M. Rassias

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Brauer Group of Moduli Spaces of Pairs

Abstract: Abstract. We show that the Brauer group of the moduli space of stable pairs with fixed determinant over a curve is zero.

Cited by 2 publications

References 13 publications

Motives and the Hodge conjecture for moduli spaces of pairs

Motives and the Hodge conjecture for moduli spaces of pairs

Rationality of the Moduli Space of Stable Pairs over a Complex Curve

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