Flat Rank Two Vector Bundles on Genus Two Curves

DOI10.1090/memo/1247zbMath1476.14003OpenAlexW4205525880MaRDI QIDQ5383921

Frank Loray, Viktoria Heu

Publication date: 20 June 2019

Published in: Memoirs of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/memo/1247

zbMATH Keywords

vector bundlesmoduli spacesHiggs bundlesKummer surfaceparabolic connections

Mathematics Subject Classification ID

Research exposition (monographs, survey articles) pertaining to algebraic geometry (14-02) Vector bundles on curves and their moduli (14H60)

Related Items

P=W conjectures for character varieties with symplectic resolution ⋮ On the moduli of logarithmic connections on elliptic curves ⋮ Geometric models and variation of weights on moduli of parabolic Higgs bundles over the Riemann sphere: a case study ⋮ A map between moduli spaces of connections ⋮ Partial algebraic solutions of isomonodromy equations on genus 2 curves ⋮ Ramified covers and tame isomonodromic solutions on curves ⋮ The Riemann-Hilbert mapping for $\mathfrak{sl}_2$ systems over genus two curves ⋮ Geometry of the moduli of parabolic bundles on elliptic curves

Cites Work

• Moduli spaces of isoperiodic forms on Riemann surfaces
• On the Hitchin system
• On the geometry of isomonodromic deformations
• A conic bundle degenerating on the Kummer surface
• Moduli of stable parabolic connections, Riemann-Hilbert correspondence and geometry of Painlevé equation of type VI. I
• Stability of rank 2 vector bundles along isomonodromic deformations
• Moduli of vector bundles on curves with parabolic structures
• Parabolic bundles, elliptic surfaces and \(SU(2)\)-representation spaces of genus zero Fuchsian groups
• Moduli of rank-2 vector bundles, theta divisors, and the geometry of curves in projective space
• Higgs bundles and local systems
• Monodromy groups and linearly polymorphic functions
• Ergodic theory on moduli spaces
• Self-duality of the \(SL_2\) Hitchin integrable system at genus 2
• Parabolic bundles as orbifold bundles
• The monodromy groups of Schwarzian equations on closed Riemann surfaces
• Invariant analytic hypersurfaces
• Spectral curves, opers and integrable systems.
• Integrable systems and algebraic surfaces
• Meromorphic connections on vector bundles over curves
• Holomorphic connections on filtered bundles over curves
• Isomonodromic deformations and Frobenius manifolds. An introduction. Transl. from the French
• Monodromy of a class of logarithmic connections on an elliptic curve
• Special coordinate coverings of Riemann surfaces
• Moduli of vector bundles on a compact Riemann surface
• On automorphism groups of ruled surfaces
• Généralisation des fonctions abéliennes
• On the logarithmic connections over curves
• Classical Algebraic Geometry
• A criterion for the existence of a flat connection on a parabolic vector bundle
• Complex Analytic Connections in Fibre Bundles
• Projective structures and projective bundles over compact Riemann surfaces
• The Self-Duality Equations on a Riemann Surface
• Holomorphic Foliations in Ruled Surfaces
• (16,6) configurations and geometry of Kummer surfaces in 𝑃³
• A Torelli Theorem for the Moduli Space of Higgs Bundles on a Curve
• Lagrangian Fibrations in Duality on Moduli Spaces of Rank 2 Logarithmic Connections Over the Projective Line
• The Riemann-Hilbert mapping for $\mathfrak{sl}_2$ systems over genus two curves
• Moduli of Semistable Logarithmic Connections
• On Weddle surfaces and their moduli
• Periods of a Moduli Space of Bundles on Curves
• Note on the structure of a ruled surface.
• Orthogonal and spin bundles over hyperelliptic curves
• Invariant vector bundles of rank 2 on hyperelliptic curves.
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