# Spectral Covers

@inproceedings{Donagi1993SpectralC, title={Spectral Covers}, author={Ron Y. Donagi}, year={1993} }

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…

## 121 Citations

PRINCIPAL BUNDLES ON ELLIPTIC FIBRATIONS *

- Mathematics
- 2016

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

- Mathematics
- 2015

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…

EQUATIONS OF THE MODULI OF HIGGS PAIRS AND INFINITE GRASSMANNIAN

- Mathematics
- 2007

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

- MathematicsProceedings 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

- Mathematics
- 1998

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

- Mathematics
- 2020

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

- Mathematics
- 2010

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

- Mathematics
- 2019

Stable, holomorphic vector bundles are constructed on an torus fibered, non-simply connected Calabi-Yau threefold using the method of bundle extensions. Since the manifold is multiply connected, we…

Pares de Higgs, grassmanniana infinita y sistemas integrables

- Mathematics
- 2008

This work makes a detailed study of Krichever's construction for several moduli spaces, which we have chosen motivated by Hitchin's Abelianization Program. In 1988, Hitchin discovered a map from the…

The Sen Limit

- Mathematics
- 2012

F-theory compactifications on elliptic Calabi-Yau manifolds may be related to IIb compactifications by taking a certain limit in complex structure moduli space, introduced by A. Sen. The limit has…

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