Cohomology of Vector Bundles and Syzygies - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Cohomology of Vector Bundles and Syzygies write by Jerzy Weyman. This book was released on 2003-06-09. Cohomology of Vector Bundles and Syzygies available in PDF, EPUB and Kindle. 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.
Vector Bundles and Representation Theory
Vector Bundles and Representation Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Vector Bundles and Representation Theory write by Steven Dale Cutkosky. This book was released on 2003. Vector Bundles and Representation Theory available in PDF, EPUB and Kindle. This volume contains 13 papers from the conference on ``Hilbert Schemes, Vector Bundles and Their Interplay with Representation Theory''. The papers are written by leading mathematicians in algebraic geometry and representation theory and present the latest developments in the field. Among other contributions, the volume includes several very impressive and elegant theorems in representation theory by R. Friedman and J. W. Morgan, convolution on homology groups of moduli spaces of sheaves on K3 surfaces by H. Nakajima, and computation of the $S1$ fixed points in Quot-schemes and mirror principle computations for Grassmanians by S.-T. Yau, et al. The book is of interest to graduate students and researchers in algebraic geometry, representation theory, topology and their applications to high energy physics.
Connections, Curvature, and Cohomology V1
Connections, Curvature, and Cohomology V1 - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Connections, Curvature, and Cohomology V1 write by . This book was released on 1972-07-31. Connections, Curvature, and Cohomology V1 available in PDF, EPUB and Kindle. Connections, Curvature, and Cohomology V1
Koszul Cohomology and Algebraic Geometry
Koszul Cohomology and Algebraic Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Koszul Cohomology and Algebraic Geometry write by Marian Aprodu. This book was released on 2010. Koszul Cohomology and Algebraic Geometry available in PDF, EPUB and Kindle. The systematic use of Koszul cohomology computations in algebraic geometry can be traced back to the foundational work of Mark Green in the 1980s. Green connected classical results concerning the ideal of a projective variety with vanishing theorems for Koszul cohomology. Green and Lazarsfeld also stated two conjectures that relate the Koszul cohomology of algebraic curves with the existence of special divisors on the curve. These conjectures became an important guideline for future research. In the intervening years, there has been a growing interaction between Koszul cohomology and algebraic geometry. Green and Voisin applied Koszul cohomology to a number of Hodge-theoretic problems, with remarkable success. More recently, Voisin achieved a breakthrough by proving Green's conjecture for general curves; soon afterwards, the Green-Lazarsfeld conjecture for general curves was proved as well. This book is primarily concerned with applications of Koszul cohomology to algebraic geometry, with an emphasis on syzygies of complex projective curves. The authors' main goal is to present Voisin's proof of the generic Green conjecture, and subsequent refinements. They discuss the geometric aspects of the theory and a number of concrete applications of Koszul cohomology to problems in algebraic geometry, including applications to Hodge theory and to the geometry of the moduli space of curves.
Syzygies
Syzygies - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Syzygies write by E. Graham Evans. This book was released on 1985-08-15. Syzygies available in PDF, EPUB and Kindle. This 1985 book covers from first principles the theory of Syzygies.
