Fibrés Paraboliques et Champ des Racines

By Niels Borne. 2006

76 citations recorded by the source corpus.

Following ideas of Nori, Biswas, ..., we show that given an integer r>0, a noetherian scheme X, and an effective Cartier divisor D on it, the parabolic vector bundles on (X,D) with weights multiples of 1/r (in the sense of Maruyama-Yokogawa) are equivalent to ordinary vector bundles on an orbifold, the stack of r-th roots associated to (X,D) (a twisted scheme in the sense of Abramovich-Vistoli). We use this fact to get some information on the finite parabolic bundles on the (pointed) projective line.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/4d9b0b80eec3c0f03eed67cac35f549e093116e4

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In Applied Mathematics

1. Carlos Simpson
2. Christian Sevenheck
3. Fabio Nironi
4. C. Hertling
5. Jarod Alper

In Geometry and Topology

1. Christian Sevenheck
2. Carlos Simpson
3. C. Hertling
4. Fabio Nironi
5. Jarod Alper
6. T. Mochizuki
7. H. Iritani

Citations in the corpus

• Moduli Spaces of Semistable Sheaves on Projective Deligne-Mumford Stacks (2008, methodology): “eligne-Mumford Stacks 3 and a parabolic Gieseker stability (see [MY92]) which is not the na¨ıve Hilbert polynomial or equivalent to a na¨ıve Gieseker stability; moreover it is proven in [MY92] and in [Bor06] that the parabolic degree can be retrieved from the parabolic Hilbert polynomial, while it i”
• Limits of families of Brieskorn lattices and compactified classifying spaces (2008, background): “orem was proved first by Borne [Bor09, th´eor`eme 2.4.20]. However, his proof is adapted to a more general situation, it is done in the algebraic category and moreover it is spread over the two papers [Bor07] and [Bor09]. Therefore we found it useful to offer here a short proof, which is actually a mi”
• Katz's middle convolution algorithm (2006, methodology): “wing Katz’s original method. If the weights of a parabolic structure are rational, i.e. for every point qi the parabolic type is a divisor concentrated over roots of unity in S1, then as discussed in [19] [27] [108] [77], the parabolic bundle may also be viewed as a bundle on a Deligne-Mumford stack”
• Local Systems on Proper Algebraic V -manifolds (2010, methodology): “Toen [103, Proposition 1.17] refers to Vistoli [112, Proof of 2.8] for this statement; see also Kresch [61].”