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Geometric properties of projective manifolds of small degree | Sijong Kwak
; Jinhyung Park
; | Date: |
12 Oct 2015 | Abstract: | 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. | Source: | arXiv, 1510.3358 | Services: | Forum | Review | PDF | Favorites |
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