<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>We 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.</p>
</abstract>

We 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.

On Chern classes of the tensor product of vector bundles

Acta Universitatis Sapientiae, Mathematica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"On Chern classes of the tensor product of vector bundles"}

We 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...

On Chern classes of the tensor product of vector bundles

Published Online: Jan 19, 2023

Page range: 330 - 340

Received: Aug 06, 2022

DOI: https://doi.org/10.2478/ausm-2022-0022

Keywords
vector bundles, Chern classes, tensor products, resultant

© 2022 Zsolt Szilágyi et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

On Chern classes of the tensor product of vector bundles

Published Online: Jan 19, 2023

Page range: 330 - 340

Received: Aug 06, 2022

DOI: https://doi.org/10.2478/ausm-2022-0022

Keywordsvector bundles, Chern classes, tensor products, resultant

© 2022 Zsolt Szilágyi et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
vector bundles, Chern classes, tensor products, resultant