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Topologically trivial sheaves on curves with simplest singularities. (English. Russian original) Zbl 1116.14029
Proc. Steklov Inst. Math. 246, 3-12 (2004); translation from Tr. Mat. Inst. Steklova 246, 10-19 (2004).
From the text: A. N. Tyurin considered in [“Quantization, classical and quantum field theory and theta functions”. CRM Monograph Series 21 (2003; Zbl 1083.14037)] a special case of topologically trivial sheaves on curves with rational irreducible components, and a trivalent dual graph.
The authors gives a construction of the moduli space $${\mathcal M}_0(X,r)$$ of topologically trivial bundles of rank $$r\geq 1$$ on a curve $$X$$, and its compactification $$\overline{\mathcal M}_0(X,r)$$, the moduli space of (semi)stable topologically trivial bundles of rank $$r\geq 1$$.
The cases $$r=1$$ of the generalized Jacobian of $$X$$ and $$\overline{\mathcal M}_0(X,2,0)$$ of rank two bundles with trivial determinant are considered in detail.
For the entire collection see [Zbl 1087.14002].

##### MSC:
 14H60 Vector bundles on curves and their moduli 14D20 Algebraic moduli problems, moduli of vector bundles