The zero set of this section consists of holomorphic maps.
2.
The composition of two holomorphic maps is holomorphic.
3.
Do you mean a subgroup of holomorphic maps?
4.
This group can be given the structure of a complex manifold in such a way that composition and inversion are holomorphic maps.
5.
:: Yes, I meant to say the subgroup whose members are holomorphic maps rather than calling the subgroup itself holomorphic.
6.
Accordingly, ?! } } is a smooth diffeomorphism, which restricts to a holomorphic map and a smooth diffeomorphism between the boundaries.
7.
"[ at the conference ] . . . Bott and I learnt of a conjecture of Shimura concerning a generalization of the Lefschetz formula for holomorphic maps.
8.
Moreover the changes of charts are holomorphic maps, more precisely maps of the form z \ mapsto z + w for some w \ in \ mathbb C.
9.
Which is defined by counting holomorphic triangles ( that is, holomorphic maps of a triangle whose vertices and edges map to the appropriate intersection points and Lagrangian submanifolds ).
10.
The Schwarz & ndash; Pick theorem then essentially states that a holomorphic map of the unit disk into itself " decreases " the distance of points in the Poincar?metric.
