Topologically trivial sheaves on curves with simplest singularities. (English. Russian original) Zbl 1116.14029

Artamkin, I. V.

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