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Record Nr. |
UNINA9910484256703321 |
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Autore |
Mochizuki Takuro <1972-> |
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Titolo |
Donaldson Type Invariants for Algebraic Surfaces : Transition of Moduli Stacks / / by Takuro Mochizuki |
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Pubbl/distr/stampa |
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Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2009 |
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ISBN |
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Edizione |
[1st ed. 2009.] |
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Descrizione fisica |
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1 online resource (XXIII, 383 p.) |
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Collana |
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Lecture Notes in Mathematics, , 1617-9692 ; ; 1972 |
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Classificazione |
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14D2014J6014J80 |
MAT 142f |
MAT 146f |
SI 850 |
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Disciplina |
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Soggetti |
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Algebraic geometry |
Algebraic Geometry |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Bibliographic Level Mode of Issuance: Monograph |
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Nota di bibliografia |
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Includes bibliographical references (p. 341-345) and index. |
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Nota di contenuto |
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Preliminaries -- Parabolic L-Bradlow Pairs -- Geometric Invariant Theory and Enhanced Master Space -- Obstruction Theories of Moduli Stacks and Master Spaces -- Virtual Fundamental Classes -- Invariants. |
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Sommario/riassunto |
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We 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! |
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