Bohr–Sommerfeld Lagrangians of moduli spaces of Higgs bundles

Biswas, Indranil; Gammelgaard, Niels Leth; Logares, Marina

doi:10.1016/j.geomphys.2015.04.005

Cited by 2 publications

(3 citation statements)

References 17 publications

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“…(3) Otherwise, we will use a field with char(K) = 2. Now we will show that any smooth core component of a weight-1 SHS is a Bohr-Sommerfeld Lagrangian, by the argument analogous to the main result of [BGL15], where the authors consider the case of Moduli spaces of Higgs bundles. We first introduce the notion of Bohr-Sommerfeld Lagrangian, which is slightly stronger than the definition 35 that can be found elsewhere.…”

Section: Symplectic Topology Of Minimal Componentsmentioning

confidence: 90%

Exact Lagrangians from contracting $\mathbb{C}^*$-actions

Živanović¹

2022

Preprint

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We obtain families of non-isotopic closed exact Lagrangian submanifolds in quasi-projective holomorphic symplectic manifolds that admit contracting C * -actions. We show that the Floer cohomologies of these Lagrangians are topological in nature, recovering the ordinary cohomologies of their intersection. Moreover, by using these Lagrangians and a version of Carrell-Goresky's integral decomposition theorem, we obtain degree-wise lower bounds on the symplectic cohomology of these spaces. Contents 1. Introduction 1 2. On semiprojective varieties 8 3. Semiprojective Holomorphic Symplectic manifolds 14 4. Symplectic structures 22 5. Smooth core components 28 6. Symplectic Topology of minimal components 33 7. Applications towards symplectic cohomology 40 References 44

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Section: Symplectic Topology Of Minimal Componentsmentioning

confidence: 90%

Exact Lagrangians from contracting $\mathbb{C}^*$-actions

Živanović¹

2022

Preprint

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“…This is a stronger condition than the Lagrangian one. For example, the only fibres in the integrable system that have this property are the components of the nilpotent cone [3].…”

Section: A General Settingmentioning

confidence: 99%

“…Since t has distinct zeros this does not lie on C 4 . Similarly if w is a section of ULK 1/2 then a 0 = ws 2 2 s 1 has a divisor with some point of multiplicity 2.…”

Section: Propositionmentioning

confidence: 99%

Spinors, Lagrangians and rank 2 Higgs bundles

Hitchin

2017

Proc. London Math. Soc.

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The paper considers the Dirac operator on a Riemann surface coupled to a symplectic holomorphic vector bundle W. Each spinor in the null-space generates through the moment map a Higgs bundle, and varying W one obtains a holomorphic Lagrangian subvariety in the moduli space of Higgs bundles. Applying this to the irreducible symplectic representations of SL(2) we obtain Lagrangian submanifolds of the rank 2 moduli space which link up with m-period points on the Prym variety of the spectral curve as well as Brill-Noether loci on the moduli space of semistable bundles. The case of genus 2 is investigated in some detail.Comment: 31 page

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Bohr–Sommerfeld Lagrangians of moduli spaces of Higgs bundles

Cited by 2 publications

References 17 publications

Exact Lagrangians from contracting $\mathbb{C}^*$-actions

Exact Lagrangians from contracting $\mathbb{C}^*$-actions

Spinors, Lagrangians and rank 2 Higgs bundles

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