Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Twisted argyle quivers and Higgs bundles   Ordinarily, quiver varieties are constructed as moduli spaces of quiver
representations in the category of vector spaces. It is also natural to
consider quiver representations in a richer category, namely that of vector
bundles on some complex variety equipped with a fixed sheaf that twists the
morphisms. Representations of A-type quivers in this twisted category --- known
in the literature as "holomorphic chains" --- have practical use in questions
concerning the topology of the moduli space of Higgs bundles. In that problem,
the variety is a Riemann surface of genus at least 2, and the twist is its
canonical line bundle. We extend the treatment of twisted A-type quiver
representations to any genus using the Hitchin stability condition induced by
Higgs bundles and computing their deformation theory. We then focus in
particular on so-called "argyle quivers", where the rank labelling alternates
between 1 and integers $r_i\geq1$. We give explicit geometric identifications
of moduli spaces of twisted representations of argyle quivers on $\mathbb{P}^1$
using invariant theory for a non-reductive action via Euclidean reduction on
polynomials. This leads to a stratification of the moduli space by change of
bundle type, which we identify with "collision manifolds" of invariant zeroes
of polynomials. We also relate the present work to Bradlow-Daskalopoulos
stability and Thaddeus' pullback maps to stable tuples. We apply our results to
computing $\mathbb{Q}$-Betti numbers of low-rank twisted Higgs bundle moduli
spaces on $\mathbb{P}^1$, where the Higgs fields take values in an arbitrary
ample line bundle. Our results agree with conjectural Poincar\'e series arising
from the ADHM recursion formula.

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The categories of this paper are: astro-ph
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The categories of this paper are: econ
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ph
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The categories of this paper are: eess
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The categories of this paper are: adap-org
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: q-alg
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The categories of this paper are: cond-mat
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The categories of this paper are: patt-sol
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-lat
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The categories of this paper are: q-fin
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The categories of this paper are: math-ph
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The categories of this paper are: q-bio