000			nam a22 4500
999			_c32781 _d32781
008			240218b xxu||||| |||| 00| 0 eng d
020			_a9783540939122
082			_a516.35 _bMOC
100			_aMochizuki, Takuro
245			_aDonaldson type invariants for algebraic surfaces : transition of moduli stacks
260			_bSpringer, _aBerlin : _c2009
300			_axxiii, 383 p. ; _bill., _c24 cm.
365			_b56.95 _c€ _d5398.86
490			_aLecture notes in mathematics _vv.1972
504			_aIncludes bibliographical references and index.
520			_aWe are defining and studying an algebro-geometric analogue of Donaldson invariants by using moduli spaces of semistable sheaves with arbitrary ranks on a polarized projective surface. We are interested in relations among the invariants, which are natural generalizations of the "wall-crossing formula" and the "Witten conjecture" for classical Donaldson invariants. Our goal is to obtain a weaker version of these relations, by systematically using the intrinsic smoothness of moduli spaces. According to the recent excellent work of L. Goettsche, H. Nakajima and K. Yoshioka, the wall-crossing formula for Donaldson invariants of projective surfaces can be deduced from such a weaker result in the rank two case!
650			_aRank Two Case
650			_aObstruction theory
650			_aSemistable sheaves
650			_aSmooth function
650			_aTransition of moduli stacks
650			_aAlgebraic surface
650			_aInvariant theory
650			_aChern class
650			_aCoherent sheaf
650			_aDonaldson invariants
650			_aHilbert polynomial
650			_aModuli stack
650			_aObstruction theory
650			_aQuasi-isomorphism
650			_aSmooth morphism
650			_aTautological line bundle
650			_aVector bundle
942			_2ddc _cBK