2011/04/02 by Chien‐Hao Liu, Chien-Hao Liu, Liu, Chien-Hao +5
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Homotopy and Cohomology in Algebraic Topology #hep-th #math.AG #math.SG #msc:14F43 #msc:14J32 #msc:14J60 #msc:57R90 #msc:81T30
paper · pdf · doi:10.48550/arxiv.1104.0280
19+1 pages
arxiv created 2011/04/02 · arxiv updated 2011/04/05
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.