LEADER 02875nam 22005655 450 001 996466482703316 005 20221020220643.0 010 $a3-540-93913-X 024 7 $a10.1007/978-3-540-93913-9 035 $a(CKB)1000000000718092 035 $a(SSID)ssj0000317288 035 $a(PQKBManifestationID)11267296 035 $a(PQKBTitleCode)TC0000317288 035 $a(PQKBWorkID)10293138 035 $a(PQKB)10150678 035 $a(DE-He213)978-3-540-93913-9 035 $a(MiAaPQ)EBC3064140 035 $a(PPN)134130839 035 $a(EXLCZ)991000000000718092 100 $a20100301d2009 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aDonaldson Type Invariants for Algebraic Surfaces$b[electronic resource] $eTransition of Moduli Stacks /$fby Takuro Mochizuki 205 $a1st ed. 2009. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2009. 215 $a1 online resource (XXIII, 383 p.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1972 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-93912-1 320 $aIncludes bibliographical references (p. 341-345) and index. 327 $aPreliminaries -- Parabolic L-Bradlow Pairs -- Geometric Invariant Theory and Enhanced Master Space -- Obstruction Theories of Moduli Stacks and Master Spaces -- Virtual Fundamental Classes -- Invariants. 330 $aWe are defining and studying an algebra-geometric analogue of Donaldson invariants by using moduli spaces of semistable sheaves with arbitrary ranks on a polarized projective surface. We are interested in relations among the invariants, which are natural generalizations of the "wall-crossing formula" and the "Witten conjecture" for classical Donaldson invariants. Our goal is to obtain a weaker version of these relations, by systematically using the intrinsic smoothness of moduli spaces. According to the recent excellent work of L. Goettsche, H. Nakajima and K. Yoshioka, the wall-crossing formula for Donaldson invariants of projective surfaces can be deduced from such a weaker result in the rank two case! 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v1972 606 $aAlgebraic geometry 606 $aAlgebraic Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M11019 615 0$aAlgebraic geometry. 615 14$aAlgebraic Geometry. 676 $a516.35 686 $a14D20$a14J60$a14J80$2msc 686 $aMAT 142f$2stub 686 $aMAT 146f$2stub 686 $aSI 850$2rvk 700 $aMochizuki$b Takuro$4aut$4http://id.loc.gov/vocabulary/relators/aut$0319920 906 $aBOOK 912 $a996466482703316 996 $aDonaldson type invariants for algebraic surfaces$9230294 997 $aUNISA