D’Angelo finite type
where ranges over all parametrized holomorphic curves (where is the unit disc) such that , is the order of vanishing at the origin, and is the composition of and . The order of vanishing is if is the smallest integer such that the th derivative of is nonzero at the origin and all derivatives of smaller order are zero at the origin. Infinity is allowed for if all derivatives vanish.
We say is of (or finite 1-type) at in the sense of D’Angelo if
If is real analytic, then is finite type at if and only if there does not exist any germ of a complex analytic subvariety at , that is contained in . If is only smooth, then it is possible that is not finite type, but does not contain a germ of a holomorphic curve. However, if is not finite type, then there exists a holomorphic curve which “touches” to infinite order.
- 1 M. Salah Baouendi, Peter Ebenfelt, Linda Preiss Rothschild. , Princeton University Press, Princeton, New Jersey, 1999.
- 2 D’Angelo, John P. , CRC Press, 1993.
|Title||D’Angelo finite type|
|Date of creation||2013-03-22 17:39:57|
|Last modified on||2013-03-22 17:39:57|
|Last modified by||jirka (4157)|