Algebraic cobordism of filtered vector bundles on varieties: Notes on a work of Lee and Pandharipande

Details Algebraic cobordism of filtered vector bundles on varieties: Notes on a work of Lee and Pandharipande Algebraic cobordism of filtered vector bundles on varieties: Notes on a work of Lee and Pandharipande

2011-04-02

arxiv.org/abs/1104.0280v1

Mathematics

Algebraic Geometry

19+1 pages

Scientific paper

The construction of double point cobordism groups of vector bundles on varieties in the work [Lee-P] (arXiv:1002.1500 [math.AG]) of Yuan-Pin Lee and Rahul Pandharipande gives immediately double point cobordism groups of filtered vector bundles on varieties. We note also that among the four basic operations -- direct sum, tensor product, dual, and Hom -- on vector bundles on varieties, only taking dual is compatible with double point cobordisms of vector bundles on varieties in general, by a demonstration on an example of vector bundles on Calabi-Yau 3-folds. A question on refined and/or higher algebraic cobordisms of vector bundles on varieties is posed in the end.

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