A Gieseker type degeneration of moduli stacks of vector bundles on curves

Details A Gieseker type degeneration of moduli stacks of vector bundles on curves A Gieseker type degeneration of moduli stacks of vector bundles on curves

2002-01-21

arxiv.org/abs/math/0201197v1

Trans. Amer. Math. Soc. 357 (2005), 4897-4955

Mathematics

Algebraic Geometry

59 pages, 10 figures

Scientific paper

Given a generically smooth stable curve over a discrete valuation ring such that its special fibre is irreducible with one double point, we construct a moduli stack over that descrete valuation ring which is a model for the moduli stack of vector bundles over the generic fibre of the curve. The model has the following nice properties: 1. It is regular. 2. Its special fibre is a normal crossing divisor. 3. The normalization of its special fibre is a locally trivial KGl-bundle over the moduli stack of vector bundles over the normalization of the special fibre of the curve. Here KGl is a canonical compactification of the general linear group. Our motivation is that such a model may help to give recursion formulae for such cohomological invariants of the moduli stack of vector bundles on smooth curves which depend only on the genus of the curve.

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