A Torelli type theorem for nodal curves. (English) Zbl 1467.14026
Summary: The moduli space of Gieseker vector bundles is a compactification of moduli of vector bundles on a nodal curve. This moduli space has only normal-crossing singularities and it provides flat degeneration of the moduli of vector bundles over a smooth projective curve. We prove a Torelli type theorem for a nodal curve using the moduli space of stable Gieseker vector bundles of fixed rank (strictly greater than \(1)\) and fixed degree such that rank and degree are co-prime.
MSC:
| 14C34 | Torelli problem |
| 14D20 | Algebraic moduli problems, moduli of vector bundles |
| 14D21 | Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) |
| 14H60 | Vector bundles on curves and their moduli |
| 14H20 | Singularities of curves, local rings |
Keywords:
algebraic geometry; moduli of vector bundles; nodal curves; torsion free sheaves; Torelli thoremReferences:
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