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Hecke modifications of vector bundles
Alvarenga, Roberto
Kaur, Inder
Moco, Leonardo
2025
Abstract
Hecke modifications of vector bundles have played a significant role in several areas of mathematics. They appear in subjects ranging from number theory to complex geometry. This article intends to be a friendly introduction to the subject. We give an overview of how Hecke modifications appear in the literature, explain their origin and their importance in number theory and classical algebraic geometry. Moreover, we report the progress made in describing Hecke modifications explicitly and why these explicit descriptions are important. We describe all the Hecke modifications of the trivial rank 2 vector bundle over a fixed point of degree 5 on the projective line, as well as all the vector bundles over a certain elliptic curve, which admit a rank 2 and degree 0 trace bundle as a Hecke modification. This result is not present in existing literature.
Publisher
EUT Edizioni Università di Trieste
Source
Roberto Alvarenga, Inder Kaur and Leonardo Moco, "Hecke modifications of vector bundles" in: "Rendiconti dell’Istituto di Matematica dell’Università di Trieste: an International Journal of Mathematics vol.57 (2025)", EUT Edizioni Università di Trieste, Trieste, 2025, pp.
Languages
en
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International
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