The Picard group of the universal moduli stack of principal bundles on pointed smooth curves

Fringuelli, Roberto; Viviani, Filippo

doi:10.48550/arxiv.2002.07494

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Using the Above Homomorphisms ω δ3

The Universal Moduli Stack Bun Ggn and Its Picard Group1

The Restriction Homomorphism1

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“…Proof. The fact that γ δ ab G ab is a well-defined homomorphism has been shown in [FVc,Prop. 4.1.2, Eq.…”

Section: The Universal Moduli Stack Bun Ggn and Its Picard Groupmentioning

confidence: 88%

“…Assume now that n = 0 and call I δ G the subgroup of NS(Bun δ G,g,n ) defined on the right hand side of (3.2.25). By [FVc,Prop. 4.3.1], we know that Im(ω δ ab G ab ⊕ γ δ ab G ab ) = I δ ab G ab .…”

Section: Using the Above Homomorphisms ω δmentioning

confidence: 99%

“…Proof. The Theorem has been proved for a torus in [FVc,Prop. 4.3.1], and we are going to apply this result for G ab in order to prove the case of a general reductive group G.…”

Section: Using the Above Homomorphisms ω δmentioning

confidence: 99%

“…Let us now prove (2). If n > 0 then ω δ ab G ab ⊕ γ δ ab G ab is surjective by [FVc,Prop. 4.3.1], which, combined with (3.2.31), implies that ω δ G ⊕ γ δ G is also surjective.…”

Section: Using the Above Homomorphisms ω δmentioning

confidence: 99%

“…Proof. The Theorem has been proved for a torus in [FVc,Prop. 4.3.3]; and, in order to prove the case of a general reductive group G, we are going to use this result for G ab and for a (fixed) maximal torus ι : T G ֒→ G.…”

Section: The Restriction Homomorphismmentioning

confidence: 99%

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The Picard group of the universal moduli space of vector bundles on stable curves

Fringuelli

2018

Advances in Mathematics

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“…Proof. The fact that γ δ ab G ab is a well-defined homomorphism has been shown in [FVc,Prop. 4.1.2, Eq.…”

Section: The Universal Moduli Stack Bun Ggn and Its Picard Groupmentioning

confidence: 88%

Section: Using the Above Homomorphisms ω δmentioning

confidence: 99%

“…Proof. The Theorem has been proved for a torus in [FVc,Prop. 4.3.1], and we are going to apply this result for G ab in order to prove the case of a general reductive group G.…”

Section: Using the Above Homomorphisms ω δmentioning

confidence: 99%

“…Let us now prove (2). If n > 0 then ω δ ab G ab ⊕ γ δ ab G ab is surjective by [FVc,Prop. 4.3.1], which, combined with (3.2.31), implies that ω δ G ⊕ γ δ G is also surjective.…”

Section: Using the Above Homomorphisms ω δmentioning

confidence: 99%

Section: The Restriction Homomorphismmentioning

confidence: 99%

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