Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geometric properties of projective manifolds of small degree   The aim of this paper is to study geometric properties of non-degenerate
smooth projective varieties of small degree from a birational point of view.
First, using the positivity property of double point divisors and the
adjunction mappings, we classify smooth projective varieties in $\mathbb P^r$
of degree $d \leq r+2$, and consequently, we show that such varieties are
simply connected and rationally connected except in a few cases. This is a
generalization of P. Ionescu's work. We also show the finite generation of Cox
rings of smooth projective varieties in $\mathbb P^r$ of degree $d \leq r$ with
counterexamples for $d=r+1, r+2$. On the other hand, we prove that a
non-uniruled smooth projective variety in $\mathbb P^r$ of dimension $n$ and
degree $d \leq n(r-n)+2$ is Calabi-Yau, and give an example that shows this
bound is also sharp.

3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs