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A support theorem for the Hitchin fibration: the case of $GL_n$ and $K_C$

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Mark Andrea A. de Cataldo, Jochen Heinloth, Luca Migliorini

Algebraic Geometry · Submitted 23 Jun 2019

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We compute the supports of the perverse cohomology sheaves of the Hitchin fibration for $GL_n$ over the locus of reduced spectral curves.

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arXiv ID1906.09582 (version 2)
Pith IDKSLH3LHX, Pith's permanent record of this paper and its review
CitationJochen Heinloth, Luca Migliorini, Mark Andrea A. de Cataldo. "A support theorem for the Hitchin fibration: the case of $GL_n$ and $K_C$." arXiv:1906.09582 (2019). https://pith.science/paper/KSLH3LHX
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,261 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.34 · human participants 0.01 · controlled comparison 0.11 · randomized assignment 0.01 · states quantitative result 0.22 · compares with prior results 0.92 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

We compute the supports of the perverse cohomology sheaves of the Hitchin fibration for $GL_n$ over the locus of reduced spectral curves. In contrast to the case of meromorphic Higgs fields we find additional supports at the loci of reducible spectral curves. Their contribution to the global cohomology is governed by a finite twist of Hitchin fibrations for Levi subgroups. The corresponding summands give non-trivial contributions to the cohomology of the moduli spaces for every $n \geq 3$. A key ingredient is a restriction result for intersection cohomology sheaves that allows us to compare the fibration to the one defined over the versal deformations of spectral curves.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We compute the supports of the perverse cohomology sheaves of the Hitchin fibration for $GL_n$ over the locus of reduced spectral curves. contribution 0.77 0.96 0.59 asserted 1.00
s1 In contrast to the case of meromorphic Higgs fields we find additional supports at the loci of reducible spectral curves. result 0.98 0.90 0.20 asserted 1.00
s2 Their contribution to the global cohomology is governed by a finite twist of Hitchin fibrations for Levi subgroups. result 0.88 0.82 0.13 asserted 1.00
s3 The corresponding summands give non-trivial contributions to the cohomology of the moduli spaces for every $n \geq 3$. result 0.96 0.85 0.20 asserted 1.00
s4 A key ingredient is a restriction result for intersection cohomology sheaves that allows us to compare the fibration to the one defined over the versal deformations of spectral curves. method 0.99 0.82 0.05 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We compute the supports of the perverse cohomology sheaves of the Hitchin fibration for $GL_n$ over the locus of reduced spectral curves. In contrast to the case of meromorphic Higgs fields we find additional supports at the loci of reducible spectral curves. Their contribution to the global cohomology is governed by a finite twist of Hitchin fibrations for Levi subgroups. The corresponding summands give non-trivial contributions to the cohomology of the moduli spaces for every $n \geq 3$. A key ingredient is a restriction result for intersection cohomology sheaves that allows us to compare the fibration to the one defined over the versal deformations of spectral curves.

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