A sequence of blowing-ups connecting moduli of sheaves and the Donaldson polynomial under change of polarization

Abstract: Let

H

and

H^{'}

be two ample line bundles over a nonsingular projective surface

X

, and

M (H)

(resp.

M (H^{'})

) the coarse moduli scheme of

H

-semistable (resp.

H^{'}

-semistable) sheaves of fixed type

(r = 2, c_{1}, c_{2})

. In a moduli-theoretic way that comes from elementary transforms, we connect

M (H)

and

M (H^{'})

by a sequence of blowing-ups when walls separating

H

and

H^{'}

are not necessarily good. As an application, we also consider the polarization change problem of Donaldson polynomials.