| 書(shū)目名稱(chēng) | Donaldson Type Invariants for Algebraic Surfaces | | 副標(biāo)題 | Transition of Moduli | | 編輯 | Takuro Mochizuki | | 視頻video | http://file.papertrans.cn/283/282593/282593.mp4 | | 概述 | Includes supplementary material: | | 叢書(shū)名稱(chēng) | Lecture Notes in Mathematics | | 圖書(shū)封面 |  | | 描述 | 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 formula” 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 | | 出版日期 | Book 2009 | | 關(guān)鍵詞 | Excel; Invariant; Natural; Obstruction theory; Semistable sheaves; Smooth function; Transition of moduli s | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-540-93913-9 | | isbn_softcover | 978-3-540-93912-2 | | isbn_ebook | 978-3-540-93913-9Series ISSN 0075-8434 Series E-ISSN 1617-9692 | | issn_series | 0075-8434 | | copyright | Springer-Verlag Berlin Heidelberg 2009 |
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