Concerning the semistability of tensor products in Arakelov geometry

TL;DR

This paper investigates the conditions under which the tensor product of hermitian vector bundles remains semistable, employing epsilon-tensor products and geometric stability concepts in Arakelov geometry.

Contribution

It introduces new methods to analyze semistability of tensor products in Arakelov geometry using epsilon-tensor products and geometric stability.

Findings

Established criteria for semistability of tensor products

Linked epsilon-tensor products with geometric stability

Provided new insights into hermitian vector bundle behavior

Abstract

We study the semistability of the tensor product of hermitian vector bundles by using the $\varepsilon$-tensor product and the geometric (semi)stability of vector subspaces in the tensor product of two vector spaces.