  This is the first part of two papers. In this part, we prove the blowup
formulae for virtual Hodge polynomials of Gieseker moduli spaces of rank-2
stable sheaves and Uhlenbeck compactification spaces over algebraic surfaces.
In particular, we verify the blowup formulae for the S-duality conjecture of
Vafa-Witten, i.e. the blowup formulae for the Euler numbers of instanton moduli
spaces over algebraic surfaces.
