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

By Chien-Hao Liu, Yu-jong Tzeng and Shing-Tung Yau

Abstract

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.Comment: 19+1 page

Topics: Mathematics - Algebraic Geometry, High Energy Physics - Theory, Mathematics - Symplectic Geometry, 14F43, 14J60, 57R90, 14J32, 81T30
Year: 2011
OAI identifier: oai:arXiv.org:1104.0280
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