Cohomology of Vector Bundles and Syzygies (Cambridge Tracts in Mathematics Book 149) 1st Edition by Jerzy Weyman (PDF)

Description

The central theme of this book is an exposition of the geometric technique of calculating syzygies. It is written from a point of view of commutative algebra, and without assuming any knowledge of representation theory the calculation of syzygies of determinantal varieties is explained. The starting point is a definition of Schur functors, and these are discussed from both an algebraic and geometric point of view. Then a chapter on various versions of Bott’s Theorem leads on to a careful explanation of the technique itself, based on a description of the direct image of a Koszul complex. Applications to determinantal varieties follow, plus there are also chapters on applications of the technique to rank varieties for symmetric and skew symmetric tensors of arbitrary degree, closures of conjugacy classes of nilpotent matrices, discriminants and resultants. Numerous exercises are included to give the reader insight into how to apply this important method.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐The epub version is virtually unreadable. The symbols are difficult to read and sometimes missing. Navigation is difficult.Added later: If you convert the background color from sepia to white and play with the text size, the legibility improves. However, the epub version was evidently produced from hard copy using optical recognition and this introduced many annoying errors such as unfinished or mangled formulas. The first such I found is on the third line of 1.1.1. Springer supplies ebooks as .pdf files; I suppose this cuts into their profit margin as there is apparently no copy protection. I personally don’t object to book publishers making a buck, but access by researchers is the most important part of the process. (See David Mumford’s comments at http://www.dam.brown.edu/people/mumford/.)Aside from the aforementioned annoyances, I found the book very helpful.

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