BROWSE

Related Scientist

Hwang, Jun Muk's photo.

Hwang, Jun Muk
복소기하학 연구단
more info

ITEM VIEW & DOWNLOAD

Unbendable rational curves of Goursat type and Cartan type

Cited 0 time in webofscience Cited 0 time in scopus
14 Viewed 0 Downloaded
Title
Unbendable rational curves of Goursat type and Cartan type
Author(s)
Jun-Muk Hwang; Qifeng Li
Publication Date
2021-11
Journal
Journal des Mathematiques Pures et Appliquees, v.155, pp.1 - 31
Publisher
Elsevier Masson s.r.l.
Abstract
© 2021 Elsevier Masson SASWe study unbendable rational curves, i.e., nonsingular rational curves in a complex manifold of dimension n with normal bundles isomorphic to OP1(1)⊕p⊕OP1⊕(n−1−p) for some nonnegative integer p. Well-known examples arise from algebraic geometry as general minimal rational curves of uniruled projective manifolds. After describing the relations between the differential geometric properties of the natural distributions on the deformation spaces of unbendable rational curves and the projective geometric properties of their varieties of minimal rational tangents, we concentrate on the case of p=1 and n≤5, which is the simplest nontrivial situation. In this case, the families of unbendable rational curves fall essentially into two classes: Goursat type or Cartan type. Those of Goursat type arise from ordinary differential equations and those of Cartan type have special features related to contact geometry. We show that the family of lines on any nonsingular cubic 4-fold is of Goursat type, whereas the family of lines on a general quartic 5-fold is of Cartan type, in the proof of which the projective geometry of varieties of minimal rational tangents plays a key role.
URI
https://pr.ibs.re.kr/handle/8788114/10608
DOI
10.1016/j.matpur.2021.05.006
ISSN
0021-7824
Appears in Collections:
Center for Complex Geometry (복소기하학 연구단) > 1. Journal Papers (저널논문)
Files in This Item:
There are no files associated with this item.

qrcode

  • facebook

    twitter

  • Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.
해당 아이템을 이메일로 공유하기 원하시면 인증을 거치시기 바랍니다.

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.

Browse