Hello everyone, I apologize for my english.

I have a little ploblem in a count:

Let Z a (Zariski) closed set in with . Consider the incidence variety and the second factor projection

.

Let smooth then proove that

is surjective if and only if , i.e. the projectif tangent space to Z at p, intersects trasversally .

Note: if (Zariski) closed, ( is the set of smooth point of Z) then Z intersects trasversally W if and only if the map

given by is surjective.

Thanks at everyone.