This book contains recent and exciting developments on the structure of moduli spaces, with an emphasis on the algebraic structures that underlie this structure. Topics covered in this title include Hilbert schemes of points, moduli of instantons, coherent sheaves and their derived categories, moduli of flat connections, Hodge structures, and the topology of affine varieties. Two beautiful series of lectures are a particularly fine feature of the book. One is an introductory series by Manfred Lehn on the topology and geometry of Hilbert schemes of points on surfaces, and the other, by Hiraku Nakajima and Kota Yoshioka, explains their recent work on the moduli space of instantons over ${\mathbb R}^4$. The material is suitable for graduate students and researchers interested in moduli spaces in algebraic geometry, topology, and mathematical physics.
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Für höhere Schule und Studium
Für Beruf und Forschung
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ISBN-13
978-0-8218-3568-5 (9780821835685)
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Schweitzer Klassifikation
Lectures on Hilbert schemes by M. Lehn Lectures on instanton counting by H. Nakajima and K. Yoshioka Hyper-Kahler Nahm transforms by C. Bartocci and M. Jardim Instanton counting via affine Lie algebras. I. Equivariant $J$-functions of (affine) flag manifolds and Whittaker vectors by A. Braverman The Gysin map is compatible with mixed Hodge structures by M. A. A. de Cataldo and L. Migliorini Representations of fundamental groups of nonorientable 2-manifolds by N.-K. Ho and L. C. Jeffrey Mukai flops and derived categories. II by Y. Namikawa Fourier-Mukai number of a K3 surface by S. Hosono, B. H. Lian, K. Oguiso, and S.-T. Yau Derived equivalence of holomorphic symplectic manifolds by J. Sawon The affine stratification number and the moduli space of curves by M. Roth and R. Vakil Coherent sheaves on generic compact tori by M. Verbitsky The cohomology rings of Hilbert schemes via Jack polynomials by W.-P. Li, Z. Qin, and W. Wang.
