# Nonexistence of exceptional bundles on $\mathbb{P}^{3}$ with maximal possible ranks

## TL;DR

This paper proves the nonexistence of certain exceptional bundles on projective 3-space with specific ranks and degrees, revealing new obstructions beyond known divisibility conditions.

## Contribution

It establishes new nonexistence results for exceptional bundles on P^3, identifying obstructions beyond the divisibility condition r|(2d^2+1).

## Key findings

- No exceptional bundles with rank 2d^2+1 and degree d for |d|4.
- Existence of no exceptional bundle with rank 27 and degree 11.
- New obstructions to the existence of exceptional bundles are identified.

## Abstract

We prove that on $\mathbb{P}^{3}$ there is no exceptional bundle with rank $r=2d^{2}+1$ and degree $d$ for every $|d|\geq 4$. In particular, we find a new obstruction for the existence of exceptional bundles other than $r|(2d^{2}+1)$. We also show that there is no exceptional bundle with rank $27$ and degree $11$ to exhibit another different obstruction.