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The Geometry of Moduli Spaces of Sheaves
Daniel HuybrechtsManfred Lehn
其他書名
A Publication of the Max-Planck-Institut für Mathematik, Bonn
出版Vieweg+Teubner Verlag, 2013-11-13
主題Technology & Engineering / GeneralTechnology & Engineering / Engineering (General)
ISBN36631162559783663116257
URLhttp://books.google.com.hk/books?id=vKXKngEACAAJ&hl=&source=gbs_api
註釋The topic of this book is the theory of semistable coherent sheaves on a smooth algebraic surface and of moduli spaces of such sheaves. The content ranges from the definition of a semistable sheaf and its basic properties over the construction of moduli spaces to the bira tional geometry of these moduli spaces. The book is intended for readers with some back ground in Algebraic Geometry, as for example provided by Hartshorne's text book [98]. There are at least three good reasons to study moduli spaces of sheaves on surfaces. Firstly, they provide examples of higher dimensional algebraic varieties with a rich and interesting geometry. In fact, in some regions in the classification of higher dimensional varieties the only known examples are moduli spaces of sheaves on a surface. The study of moduli spaces therefore sheds light on some aspects of higher dimensional algebraic geometry. Secondly, moduli spaces are varieties naturally attached to any surface. The understanding of their properties gives answers to problems concerning the geometry of the surface, e. g. Chow group, linear systems, etc. From the mid-eighties till the mid-nineties most of the work on moduli spaces of sheaves on a surface was motivated by Donaldson's ground breaking re sults on the relation between certain intersection numbers on the moduli spaces and the dif ferentiable structure of the four-manifold underlying the surface.