Moving poles of meromorphic linear systems on ℙ1(ℂ) in the complex plane

Theoretical and Mathematical Physics. 2010. Vol. 165. No. 3. P. 1637–1649.

V. A. Poberezhny, Helminck G. F.

Let E 0 be a holomorphic vector bundle over P1(C) and †0 be a meromorphic connection of E 0. We introduce the notion of an integrable connection that describes the movement of the poles of †0 in the complex plane with integrability preserved. We show the that such a deformation exists under sufficiently weak conditions on the deformation space. We also show that if the vector bundle E0 is trivial, then the solutions of the corresponding nonlinear equations extend meromorphically to the deformation space.

Ключевые слова: integrable connection, integrable deformation, deformation space, logarithmic pole, интегрируемая связность, интегрируемая деформация, деформационное пространство, логарифмический полюс