02875nam 22005655 450 99646648270331620221020220643.03-540-93913-X10.1007/978-3-540-93913-9(CKB)1000000000718092(SSID)ssj0000317288(PQKBManifestationID)11267296(PQKBTitleCode)TC0000317288(PQKBWorkID)10293138(PQKB)10150678(DE-He213)978-3-540-93913-9(MiAaPQ)EBC3064140(PPN)134130839(EXLCZ)99100000000071809220100301d2009 u| 0engurnn#008mamaatxtccrDonaldson Type Invariants for Algebraic Surfaces[electronic resource] Transition of Moduli Stacks /by Takuro Mochizuki1st ed. 2009.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,2009.1 online resource (XXIII, 383 p.)Lecture Notes in Mathematics,0075-8434 ;1972Bibliographic Level Mode of Issuance: Monograph3-540-93912-1 Includes bibliographical references (p. 341-345) and index.Preliminaries -- Parabolic L-Bradlow Pairs -- Geometric Invariant Theory and Enhanced Master Space -- Obstruction Theories of Moduli Stacks and Master Spaces -- Virtual Fundamental Classes -- Invariants.We are defining and studying an algebra-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!Lecture Notes in Mathematics,0075-8434 ;1972Algebraic geometryAlgebraic Geometryhttps://scigraph.springernature.com/ontologies/product-market-codes/M11019Algebraic geometry.Algebraic Geometry.516.3514D2014J6014J80mscMAT 142fstubMAT 146fstubSI 850rvkMochizuki Takuroauthttp://id.loc.gov/vocabulary/relators/aut319920BOOK996466482703316Donaldson type invariants for algebraic surfaces230294UNISA