Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ulrich Bundles on Projective Spaces   We assume that $\mathcal{E}$ is a rank $r$ Ulrich bundle for $(P^n,
\mathcal{O}(d))$. The main result of this paper is that $\mathcal{E}(i)\otimes
\Omega^{j}(j)$ has natural cohomology for any integers $i \in \mathbb{Z}$ and
$0 \leq j \leq n$, and every Ulrich bundle $\mathcal{E}$ has a resolution in
terms of $n$ of the trivial bundle over $P^n$. As a corollary, we can give a
necessary and sufficient condition for Ulrich bundles if $n \leq 3$, which can
be used to find some new examples, i.e., rank $2$ bundles for $(P^3,
\mathcal{O}(2))$ and rank $3$ bundles for $(P^2, \mathcal{O}(3))$.

20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con