Equations of the Moduli of Higgs Pairs and Infinite Grassmannian

Serrano, Daniel Hernández; Porras, J. M. Muñoz; Martı́n, Francisco

doi:10.1142/s0129167x09005637

Cited by 5 publications

(3 citation statements)

References 10 publications

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“…We also note that many topics of this paper have been studied by the Salamanca school of algebraic geometers from yet another point of view [2,7,9,22].…”

Section: Cymentioning

confidence: 99%

Hitchin integrable systems, deformations of spectral curves, and KP-type equations

Hodge¹,

Mulase²

2008

Preprint

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An effective family of spectral curves appearing in Hitchin fibrations is determined. Using this family the moduli spaces of stable Higgs bundles on an algebraic curve are embedded into the Sato Grassmannian. We show that the Hitchin integrable system, the natural algebraically completely integrable Hamiltonian system defined on the Higgs moduli space, coincides with the KP equations. It is shown that the Serre duality on these moduli spaces corresponds to the formal adjoint of pseudo-differential operators acting on the Grassmannian. From this fact we then identify the Hitchin integrable system on the moduli space of Sp 2m -Higgs bundles in terms of a reduction of the KP equations. We also show that the dual Abelian fibration (the SYZ mirror dual) to the Sp 2m -Higgs moduli space is constructed by taking the symplectic quotient of a Lie algebra action on the moduli space of GL-Higgs bundles.

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“…We also note that many topics of this paper have been studied by the Salamanca school of algebraic geometers from yet another point of view [2,7,9,22].…”

Section: Cymentioning

confidence: 99%

Hitchin integrable systems, deformations of spectral curves, and KP-type equations

Hodge¹,

Mulase²

2008

Preprint

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“…In particular, in the papers [33,34,35] it was shown that, the so-called Schur pair plays a central role in the construction and analysis of Krichever map. With all the diversity of the results obtained, the constructions associated with the Krichever map share a common feature, namely, an algebraic curve, though closely connected, is, essentially, an object exterior to Sato Grassmannian except, probably the rather formal papers [36,20]. It seems that there are very few results concerning the study of algebraic curves in Sato Grassmannian itself.…”

mentioning

confidence: 99%

“…It should be noted that the main scope of the paper is a search of concrete algebraic curves and corresponding families in the specific Birkhoff strata of Sato Grassmannian in contrast to the general and formal description addressed in the papers [34,36,20,33,35].…”

mentioning

confidence: 99%

Birkhoff Strata of Sato Grassmannian and Algebraic Curves

Konopelchenko

Ortenzi

2021

JNMP

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Algebraic and geometric structures associated with Birkhoff strata of Sato Grassmannian are analyzed. It is shown that each Birkhoff stratum ΣS contains a subset W S of points for which each fiber of the corresponding tautological subbundle T BW S is closed with respect to multiplication. Algebraically T BW S is an infinite family of infinite-dimensional commutative associative algebras and geometrically it is an infinite tower of families of algebraic curves. For the big cell the subbundle T BW ∅ represents the tower of families of normal rational (Veronese) curves of all degrees. For W1 such tautological subbundle is the family of coordinate rings for elliptic curves. For higher strata, the subbundles T BW 1,2,...,n represent families of plane (n + 1, n + 2) curves (trigonal curves at n = 2) and space curves of genus n. Two methods of regularization of singular curves contained in T BW S , namely, the standard blowing-up and transition to higher strata with the change of genus are discussed.

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Coverings with prescribed ramification and Virasoro groups

Porras¹,

Martı́n²

2010

Kyoto J. Math.

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Equations of the Moduli of Higgs Pairs and Infinite Grassmannian

Cited by 5 publications

References 10 publications

Hitchin integrable systems, deformations of spectral curves, and KP-type equations

Hitchin integrable systems, deformations of spectral curves, and KP-type equations

Birkhoff Strata of Sato Grassmannian and Algebraic Curves

Coverings with prescribed ramification and Virasoro groups

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