# 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 *

- 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…

Taniguchi Lecture on Principal Bundles on Elliptic Fibrations

- Physics, 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, Physics
- 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…

E8 spectral curves

- Mathematics, Physics
- 2020

I provide an explicit construction of spectral curves for the affine $\mathrm{E}_8$ relativistic Toda chain. Their closed form expression is obtained by determining the full set of character…

Moduli of parabolic Higgs bundles and Atiyah algebroids

- Mathematics, Physics
- 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

- 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

- Physics, 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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