Geometric properties of projective manifolds of small degree

Cited 0 time in webofscience Cited 0 time in scopus
  • Hit : 468
  • Download : 0
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 P-r of degree d <= r + 2, and consequently, we show that such varieties are simply connected and rationally connected except in a few cases. This is a generalisation of P. Ionescu's work. We also show the finite generation of Cox rings of smooth projective varieties in P-r of degree d <= r with counterexamples for d = r + 1, r + 2. On the other hand, we prove that a non-uniruled smooth projective variety in P-r of dimension n and degree d <= n(r - n) + 2 is Calabi-Yau, and give an example that shows this bound is also sharp
Publisher
CAMBRIDGE UNIV PRESS
Issue Date
2016-03
Language
English
Article Type
Article
Keywords

MORI DREAM SPACES; VECTOR-BUNDLES; MINIMAL MODELS; GREATER-THAN; FANO 3-FOLDS; VARIETIES; SURFACES; CLASSIFICATION; CODIMENSION; CONJECTURE

Citation

MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, v.160, no.2, pp.257 - 277

ISSN
0305-0041
DOI
10.1017/S0305004115000663
URI
http://hdl.handle.net/10203/212500
Appears in Collection
MA-Journal Papers(저널논문)
Files in This Item
There are no files associated with this item.

qr_code

  • mendeley

    citeulike


rss_1.0 rss_2.0 atom_1.0