• Corpus ID: 16347090

Spectral Covers

  title={Spectral Covers},
  author={Ron Y. Donagi},
Spectral curves arose historically out of the study of differential equations of Lax type. Following Hitchin’s work [H1], they have acquired a central role in understanding the moduli spaces of vector bundles and Higgs bundles on a curve. Simpson’s work [S] suggests a similar role for spectral covers S̃ of higher dimensional varieties S in moduli questions for bundles on S. The purpose of these notes is to combine and review various results about spectral covers, focusing on the decomposition… 
A central role in recent investigations of the duality of F-theory and heterotic strings is played by the moduli of principal bundles, with various structure groups G, over an elliptically fibered
Semistable rank 2 co-Higgs bundles over Hirzebruch surfaces
It has been observed by S. Rayan that the complex projective surfaces that potentially admit non-trivial examples of semistable co-Higgs bundles must be found at the lower end of the Enriques-Kodaira
In this paper the moduli space of Higgs pairs over a fixed smooth projective curve with extra formal data is defined and is endowed with a scheme structure. We introduce a relative version of the
E8 spectral curves
  • A. Brini
  • Mathematics
    Proceedings of the London Mathematical Society
  • 2020
I provide an explicit construction of spectral curves for the affine E8 relativistic Toda chain. Their closed‐form expression is obtained by determining the full set of character relations in the
Taniguchi Lecture on Principal Bundles on Elliptic Fibrations
In this talk we discuss the description of the moduli space of principal G-bundles on an elliptic fibration X-->S in terms of cameral covers and their distinguished Prym varieties. We emphasize the
Discriminant and Hodge classes on the space of Hitchin covers
We continue the study of the rational Picard group of the moduli space of Hitchin spectral covers started in Korotkin and Zograf (J Math Phys 59(9):091412, 2018). In the first part of the paper we
Moduli of parabolic Higgs bundles and Atiyah algebroids
Abstract In this paper we study the geometry of the moduli space of (non-strongly) parabolic Higgs bundles over a Riemann surface with marked points. We show that this space possesses a Poisson
Sheaf Cohomology, and the Heterotic Standard Model
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Pares de Higgs, grassmanniana infinita y sistemas integrables
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The Sen Limit
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A Non-Linear Deformation of the Hitchin Dynamical System
Mukai's space, parametrizing simple sheaves on a K3 surface S whose numerical invariants are those of a line bundle on a curve C in S, is interpreted as a deformation of Hitchin's system on C. This
Spectral curves and the generalised theta divisor.
Let X be a smooth, irreducible, projective curve over an algebraically closed field of characteristic 0 and let g = gx ̂ 2 be its genus. We show in this paper that a generic vector b ndle on X of
Geometric quantization of Chern-Simons gauge theory
We present a new construction of the quantum Hubert space of ChernSimons gauge theory using methods which are natural from the threedimensional point of view. To show that the quantum Hubert space
Cubics, Integrable Systems, and Calabi-Yau Threefolds
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Group-Theoretical Methods in the Theory of Finite-Dimensional Integrable Systems
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The tetragonal construction
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Using the space of holomorphic symmetric tensors on the moduli space of stable bundles over a Riemann surface we construct a projectively flat connection on a vector bundle over Teichmüller space.