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/lp/de-gruyter/on-chern-classes-of-the-tensor-product-of-vector-bundles-y0sI7bJQ7H
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- Publisher
- de Gruyter
- Copyright
- © 2022 Zsolt Szilágyi et al., published by Sciendo
- eISSN
- 2066-7752
- DOI
- 10.2478/ausm-2022-0022
- Publisher site
- See Article on Publisher Site
Abstract
AbstractWe present two formulas for Chern classes (polynomial) of the tensor product of two vector bundles. In the first formula the Chern polynomial of the product is expressed as determinant of a polynomial in a matrix variable involving the Chern classes of the first bundle with Chern classes of the second bundle as coefficients. In the second formula the total Chern class of the tensor product is expressed as resultant of two explicit polynomials. Finally, formulas for the total Chern class of the second symmetric and the second alternating products are deduced.
Journal
Acta Universitatis Sapientiae, Mathematica – de Gruyter
Published: Dec 1, 2022
Keywords: vector bundles; Chern classes; tensor products; resultant; 14C17; 05E05