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Donaldson Type Invariants for Algebraic Surfaces
Transition of Moduli Stacks
Taschenbuch von Takuro Mochizuki
Sprache: Englisch

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Beschreibung
In this monograph, we de?ne and investigate an algebro-geometric analogue of Donaldson invariants by using moduli spaces of semistable sheaves with arbitrary ranks on a polarized projective surface. We may expect the existence of interesting ¿universal relations among invariants¿, which would be a natural generalization of the ¿wall-crossing formulä and the ¿Witten conjecture¿ for classical Donaldson invariants. Our goal is to obtain a weaker version of such relations, in other brief words, to describe a relation as the sum of integrals over the products of m- uli spaces of objects with lower ranks. Fortunately, according to a recent excellent work of L. Gottsche, ¿ H. Nakajima and K. Yoshioka, [53], a wall-crossing formula for Donaldson invariants of projective surfaces can be deduced from such a weaker result in the rank two case. We hope that our work in this monograph would, at least tentatively, provides a part of foundation for the further study on such universal relations. In the rest of this preface, we would like to explain our motivation and some of important ingredients of this study. See Introduction for our actual problems and results. Donaldson Invariants Let us brie?y recall Donaldson invariants. We refer to [22] for more details and precise. We also refer to [37], [39], [51] and [53]. LetX be a compact simply con- ? nected oriented real 4-dimensional C -manifold with a Riemannian metric g. Let P be a principalSO(3)-bundle on X.
In this monograph, we de?ne and investigate an algebro-geometric analogue of Donaldson invariants by using moduli spaces of semistable sheaves with arbitrary ranks on a polarized projective surface. We may expect the existence of interesting ¿universal relations among invariants¿, which would be a natural generalization of the ¿wall-crossing formulä and the ¿Witten conjecture¿ for classical Donaldson invariants. Our goal is to obtain a weaker version of such relations, in other brief words, to describe a relation as the sum of integrals over the products of m- uli spaces of objects with lower ranks. Fortunately, according to a recent excellent work of L. Gottsche, ¿ H. Nakajima and K. Yoshioka, [53], a wall-crossing formula for Donaldson invariants of projective surfaces can be deduced from such a weaker result in the rank two case. We hope that our work in this monograph would, at least tentatively, provides a part of foundation for the further study on such universal relations. In the rest of this preface, we would like to explain our motivation and some of important ingredients of this study. See Introduction for our actual problems and results. Donaldson Invariants Let us brie?y recall Donaldson invariants. We refer to [22] for more details and precise. We also refer to [37], [39], [51] and [53]. LetX be a compact simply con- ? nected oriented real 4-dimensional C -manifold with a Riemannian metric g. Let P be a principalSO(3)-bundle on X.
Zusammenfassung

Includes supplementary material: [...]

Inhaltsverzeichnis
Preliminaries.- Parabolic L-Bradlow Pairs.- Geometric Invariant Theory and Enhanced Master Space.- Obstruction Theories of Moduli Stacks and Master Spaces.- Virtual Fundamental Classes.- Invariants.
Details
Erscheinungsjahr: 2009
Fachbereich: Arithmetik & Algebra
Genre: Mathematik, Medizin, Naturwissenschaften, Technik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Inhalt: xxiii
383 S.
ISBN-13: 9783540939122
ISBN-10: 3540939121
Sprache: Englisch
Herstellernummer: 12463930
Einband: Kartoniert / Broschiert
Autor: Mochizuki, Takuro
Hersteller: Springer Berlin
Springer Berlin Heidelberg
Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße: 235 x 155 x 23 mm
Von/Mit: Takuro Mochizuki
Erscheinungsdatum: 27.03.2009
Gewicht: 0,628 kg
Artikel-ID: 101664483
Zusammenfassung

Includes supplementary material: [...]

Inhaltsverzeichnis
Preliminaries.- Parabolic L-Bradlow Pairs.- Geometric Invariant Theory and Enhanced Master Space.- Obstruction Theories of Moduli Stacks and Master Spaces.- Virtual Fundamental Classes.- Invariants.
Details
Erscheinungsjahr: 2009
Fachbereich: Arithmetik & Algebra
Genre: Mathematik, Medizin, Naturwissenschaften, Technik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Inhalt: xxiii
383 S.
ISBN-13: 9783540939122
ISBN-10: 3540939121
Sprache: Englisch
Herstellernummer: 12463930
Einband: Kartoniert / Broschiert
Autor: Mochizuki, Takuro
Hersteller: Springer Berlin
Springer Berlin Heidelberg
Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße: 235 x 155 x 23 mm
Von/Mit: Takuro Mochizuki
Erscheinungsdatum: 27.03.2009
Gewicht: 0,628 kg
Artikel-ID: 101664483
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