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In a series of two articles Kebekus studied deformation theory of
minimal rational curves on contact Fano manifolds. Such curves are called contact
lines. Kebekus proved that a contact line through a general point is necessarily
smooth and has a fixed standard splitting type of the restricted tangent bundle. In
this paper we study singular contact lines and those with special splitting type. We
provide restrictions on the families of such lines, and on contact Fano manifolds
which have reducible varieties of minimal rational tangents. We also show that
the results about singular lines naturally generalise to complex contact manifolds,
which are not necessarily Fano, for instance, quasi-projective contact manifolds
or compact contact manifolds of Fujiki class C. In particular, in many cases the
dimension of a family of singular lines is at most 2 less than the dimension of the
contact manifold.
słowa kluczowe w j. angielskim:
complex contact manifold, minimal rational curves, contact lines, VMRT, manifolds of Fujiki class C
wydział: instytut / zakład / katedra:
Wydział Matematyki i Informatyki : Instytut Matematyki