Uniform Steiner bundles

TL;DR

This paper investigates $k$-type uniform Steiner bundles, establishing bounds for rank when $k=1$, providing examples, and proposing a conjecture that all such bundles can be constructed via a specific method.

Contribution

It introduces bounds for the rank of $k$-type uniform Steiner bundles, offers explicit examples for each possible rank, and conjectures a construction method for all such bundles.

Findings

Sharp bounds for rank when $k=1$

Explicit families of examples for each allowed rank

Conjecture on construction of all $k$-type uniform Steiner bundles

Abstract

In this work we study $k$-type uniform Steiner bundles, being $k$ the lowest degree of the splitting. We prove sharp upper and lower bounds for the rank in the case $k=1$ and moreover we give families of examples for every allowed possible rank and explain which relation exists between the families. After dealing with the case $k$ in general, we conjecture that every $k$-type uniform Steiner bundle is obtained through the proposed construction technique.