?? "weil restriction" ... ???... ?? does this ever take complex projective varieties to real affine ones ??? .....

?? ... confusion about this ... ???? ??? relationship of weil restriction to idea of associating to complex projective variety real affine variety of nice projection operators canonically associated to points of projective space ... ??? does this actually make any sense ??, is there actually such a canonical association ?? ... ??? ....

?? vs ... ???confusion between real affine and real projective varies which superficially look similar ... "circle" vs "projective line" ... ????... ??? understood this to some extent but seems hazy now ... ?? as does previous paragraph ?? .... ??? ....