ترغب بنشر مسار تعليمي؟ اضغط هنا

Rational curves and prolongations of G-structures

105   0   0.0 ( 0 )
 نشر من قبل Jun-Muk Hwang
 تاريخ النشر 2017
  مجال البحث
والبحث باللغة English
 تأليف Jun-Muk Hwang




اسأل ChatGPT حول البحث

In a joint work with N. Mok in 1997, we proved that for an irreducible representation $G subset {bf GL}(V),$ if a holomorphic $G$-structure exists on a uniruled projective manifold, then the Lie algebra of $G$ has nonzero prolongation. We tried to generalize this to an arbitrary connected algebraic subgroup $G subset {bf GL}(V)$ and a complex manifold containing an immersed rational curve, but the proposed proof had a flaw.



قيم البحث

اقرأ أيضاً

We provide an algorithm to check whether two rational space curves are related by a similarity. The algorithm exploits the relationship between the curvatures and torsions of two similar curves, which is formulated in a computer algebra setting. Heli cal curves, where curvature and torsion are proportional, need to be distinguished as a special case. The algorithm is easy to implement, as it involves only standard computer algebra techniques, such as greatest common divisors and resultants, and Grobner basis for the special case of helical curves. Details on the implementation and experimentation carried out using the computer algebra system Maple 18 are provided.
221 - Lei Fu , Wei Li 2019
In this paper, we study unirational differential curves and the corresponding differential rational parametrizations. We first investigate basic properties of proper differential rational parametrizations for unirational differential curves. Then we show that the implicitization problem of proper linear differential rational parametric equations can be solved by means of differential resultants. Furthermore, for linear differential curves, we give an algorithm to determine whether an implicitly given linear differential curve is unirational and, in the affirmative case, to compute a proper differential rational parametrization for the differential curve.
109 - Jun-Muk Hwang , Qifeng Li 2021
We study unbendable rational curves, i.e., nonsingular rational curves in a complex manifold of dimension $n$ with normal bundles isomorphic to $mathcal{O}_{mathbb{P}^1}(1)^{oplus p} oplus mathcal{O}_{mathbb{P}^1}^{oplus (n-1-p)}$ for some nonnegativ e 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 $n leq 5$, 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.
278 - Michel Brion , Baohua Fu 2015
Consider a simple algebraic group G of adjoint type, and its wonderful compactification X. We show that X admits a unique family of minimal rational curves, and we explicitly describe the subfamily consisting of curves through a general point. As an application, we show that X has the target rigidity property when G is not of type A_1 or C.
138 - Jun-Muk Hwang 2020
We study a cone structure ${mathcal C} subset {mathbb P} D$ on a holomorphic contact manifold $(M, D subset T_M)$ such that each fiber ${mathcal C}_x subset {mathbb P} D_x$ is isomorphic to a Legendrian submanifold of fixed isomorphism type. By chara cterizing subadjoint varieties among Legendrian submanifolds in terms of contact prolongations, we prove that the canonical distribution on the associated contact G-structure admits a holomorphic horizontal splitting.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا