Critical Loci for Higgs Bundles

Hitchin, Nigel

doi:10.1007/s00220-019-03336-4

Cited by 21 publications

(20 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As the smooth locus of every component with its reduced structure deforms from the Mukai to the Hitchin system, the multiplicities and degrees must coincide. Here, indeed, the same multiplicities can be found in [23,Propositions 34 and 35] and [15,Proposition 6], whereas, up to our knowledge, the degrees have not been determined in the literature. In our case, the degrees determine the multiplicities.…”

Section: Theorem 11 Let C ∈ |H | Be An Irreducible Curve the Degreesupporting

confidence: 74%

The nilpotent cone in the Mukai system of rank two and genus two

Hellmann

2021

Math. Ann.

View full text Add to dashboard Cite

show abstract

Section: Theorem 11 Let C ∈ |H | Be An Irreducible Curve the Degreesupporting

confidence: 74%

The nilpotent cone in the Mukai system of rank two and genus two

Hellmann

2021

Math. Ann.

View full text Add to dashboard Cite

show abstract

“…This result was proved in [40,Proposition 6] for SL 2 Higgs bundles (i even) and for twisted SL 2 Higgs bundles (i odd) in [33].…”

Section: Corollary 510mentioning

confidence: 80%

“…pairs (E, ) with ∈ H 0 (C; End(E) ⊗ K ). It was constructed in Hitchin [40] by gauge theoretic and in [57,64] by algebraic geometric techniques. Pauly and Péon-Nieto [58] proved that E is very stable if and only if…”

Section: Introductionmentioning

confidence: 99%

Very stable Higgs bundles, equivariant multiplicity and mirror symmetry

Hausel

Hitchin

2022

Invent. math.

Self Cite

View full text Add to dashboard Cite

We define and study the existence of very stable Higgs bundles on Riemann surfaces, how it implies a precise formula for the multiplicity of the very stable components of the global nilpotent cone and its relationship to mirror symmetry. The main ingredients are the Bialynicki-Birula theory of $${\mathbb {C}}^*$$ C ∗ -actions on semiprojective varieties, $${\mathbb {C}}^*$$ C ∗ characters of indices of $${\mathbb {C}}^*$$ C ∗ -equivariant coherent sheaves, Hecke transformation for Higgs bundles, relative Fourier–Mukai transform along the Hitchin fibration, hyperholomorphic structures on universal bundles and cominuscule Higgs bundles.

show abstract

“…3. What is the connection, if any, between the divisors appearing in this work and the "critical loci" discussed in the recent paper of N.Hitchin [19]? Remark 7.1.…”

Section: Open Questionsmentioning

confidence: 89%

Tau functions, Hodge classes, and discriminant loci on moduli spaces of Hitchin’s spectral covers

Korotkin

Zograf

2018

Journal of Mathematical Physics

View full text Add to dashboard Cite

We define two tau functions, τ andτ , on moduli spaces of spectral covers of GL(n) Hitchin's systems. Analyzing the properties of τ , we express the divisor class of the universal Hitchin's discriminant in terms of standard generators of the rational Picard group of the moduli spaces of spectral covers with variable base. The functionτ is used to compute the divisor of canonical 1-forms with multiple zeros.

show abstract

Critical Loci for Higgs Bundles

Cited by 21 publications

References 25 publications

The nilpotent cone in the Mukai system of rank two and genus two

The nilpotent cone in the Mukai system of rank two and genus two

Very stable Higgs bundles, equivariant multiplicity and mirror symmetry

Tau functions, Hodge classes, and discriminant loci on moduli spaces of Hitchin’s spectral covers

Contact Info

Product

Resources

About