**Problem -99**
Suppose

*G* is a semi-simple algebraic group over

,

*P* *G* a maximal parabolic subgroup,

*Y* =

*G*/

*P*. Let

*f* :

*Y**X* be a finite, surjective morphism of degree > 1
to a smooth variety

*X*; then is

*X* ^{n}?
(

*n* = dim

*X* = dim

*Y*)

**Theorem 1**
Let

*Q* be a smooth quadric hypersurface in

^{n + 1}, where

*n* = 2

*k* + 1.
Then for any positive integer

*d* 0 (

*mod* 2

^{k}) there exist
continuous maps

*f* :

^{n}*Q* satisfying

*f*^{*}(

(1)) =

(

*d* ).

**Theorem 2**
Let

*Q* be a smooth quadric hypersurface in

^{n + 1}. Then there exists
a positive integer

*m* and continuous maps
of degree
(

*m*^{ . }*d* )

^{n} from

*Q* to

*Q*, for all

*d* .