Brauer obstruction for a universal vector bundle

Balaji, V.; Biswas, Indranil; Gabber, Ofer; Nagaraj, D. S.

doi:10.1016/j.crma.2007.07.011

Cited by 32 publications

(45 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…If a 1 = 1 (see (1.2)), then PM α s coincides with the moduli space of stable vector bundles of rank n and determinant L, and the Brauer group of it is already computed in [3]. Hence we will assume that a 1 > 1.…”

Section: One Parabolic Point and Small Parabolic Weightsmentioning

confidence: 99%

Brauer group of a moduli space of parabolic vector bundles over a curve

Biswas¹,

Dey²

2011

J. K-Theory

Self Cite

View full text Add to dashboard Cite

Abstract. Let PM α s be a moduli space of stable parabolic vector bundles of rank n ≥ 2 and fixed determinant of degree d over a compact connected Riemann surface X of genus g(X) ≥ 2. If g(X) = 2, then we assume that n > 2. Let m denote the greatest common divisor of d, n and the dimensions of all the successive quotients of the quasi-parabolic filtrations. We prove that the Brauer group Br(PM α s ) is isomorphic to the cyclic group Z/mZ. We also show that Br(PM α s ) is generated by the Brauer class of the Brauer-Severi variety over PM α s obtained by restricting the universal projective bundle over X × PM α s .

show abstract

Section: One Parabolic Point and Small Parabolic Weightsmentioning

confidence: 99%

Brauer group of a moduli space of parabolic vector bundles over a curve

Biswas¹,

Dey²

2011

J. K-Theory

Self Cite

View full text Add to dashboard Cite

show abstract

“…We will show that the theorem follows from (3.5) if we use [2]. From Proposition 3.2 we know that cl(P 0 ) = cl(P x ), and from [2, Proposition 1.2(a)] we know that cl(P x ) generates Br(M(r, Λ)).…”

Section: Brauer Groupmentioning

confidence: 97%

“…Since Br(M τ (r, Λ)) is independent of τ , this completes the proof using [2]. But we shall give a different proof without using [2], because we want to show that the above mentioned result of [2] can be deduced from our Let us now investigate the missing case of (r, g, d) = (3, 2, 2k).…”

Section: Brauer Groupmentioning

confidence: 99%

See 1 more Smart Citation

Brauer Group of Moduli Spaces of Pairs

Biswas

Logares

Muñoz

2012

Communications in Algebra

Self Cite

View full text Add to dashboard Cite

show abstract

“…The Brauer group Br(M (r, Λ)) is generated by the Brauer class cl(P x ) of the projective bundle P x (cf. [1]). On the other hand, we have an exact sequence [1]).…”

Section: Rationality For D Largementioning

confidence: 99%

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

Biswas

Logares

Muñoz

2012

Springer Optimization and Its Applications

Self Cite

View full text Add to dashboard Cite

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

show abstract

Brauer obstruction for a universal vector bundle

Cited by 32 publications

References 5 publications

Brauer group of a moduli space of parabolic vector bundles over a curve

Brauer group of a moduli space of parabolic vector bundles over a curve

Brauer Group of Moduli Spaces of Pairs

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

Contact Info

Product

Resources

About