Counting Higgs bundles and type quiver bundles
نویسندگان
چکیده
منابع مشابه
Homological algebra of quiver bundles
The category of representations of a finite quiver in the category of sheaves of modules on a ringed space is abelian. We show that this category has enough injectives by constructing an explicit injective resolution. From this resolution we deduce a long exact sequence relating the Ext groups in these two categories. We also show that under some hypotheses, the Ext groups are isomorphic to cer...
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H(X,C) = H(X)⊕H(X) = H(X,OX)⊕H(X,ΩX). Therefore, homomorphisms π1(X) → C are the same as an element of H(X,OX), i.e. a holomorphic line bundle of degree 0, and an element of H(X,ΩX), i.e. a holomorphic 1-form. In these notes, we describe an analogous correspondence for the case of represenations into a nonabelian Lie Group G, focusing in particular on the case G = GL(n,C) [5]. Theorems are give...
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It is known that the Seiberg-Witten invariants, derived from supersymmetric Yang-Mill theories in four-dimensions, do not distinguish smooth structure of certain non-simply-connected four manifolds. We propose generalizations of Donaldson-Witten and Vafa-Witten theories on a Kähler manifold based on Higgs Bundles. We showed, in particular, that the partition function of our generalized Vafa-Wit...
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For a complex manifold X which has a holomorphic form ̟ of odd degree k, we endow E = ⊕ p≥a Λ (p,0)(X) with a Higgs bundle structure θ given by θ(Z)(φ) := {i(Z)̟} ∧ φ. The properties such as curvature and stability of these and other Higgs bundles are examined. We prove (Theorem 2, section 2, for k > 1) E and additional classes of Higgs subbundles of E do not admit Higgs-Hermitian-Yang-Mills metr...
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ژورنال
عنوان ژورنال: Compositio Mathematica
سال: 2020
ISSN: 0010-437X,1570-5846
DOI: 10.1112/s0010437x20007010