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The articles in this volume are devoted to: - moduli of coherent sheaves; - principal bundles and sheaves and their moduli; - new insights into Geometric Invariant Theory; - stacks of shtukas and their compactifications; - algebraic cycles vs. commutative algebra; - Thom polynomials of singularities; - zero schemes of sections of vector bundles. The main purpose is to give "friendly" introductions to the above topics through a series of comprehensive texts starting from a very elementary level and ending with a discussion of current research. In these texts, the reader will find classical results and methods as well as new ones. The book is addressed to researchers and graduate students in algebraic geometry, algebraic topology and singularity theory. Most of the material presented in the volume has not appeared in books before. Contributors: Jean-Marc Drézet, Tomás L. Gómez, Adrian Langer, Piotr Pragacz, Alexander H. W. Schmitt, Vasudevan Srinivas, Ngo Dac Tuan, Andrzej Weber.

Algebraic cycles. --- Moduli theory. --- Sheaf theory. --- Vector bundles. --- Hoene-Wroński, Józef Maria, --- Fiber spaces (Mathematics) --- Cohomology, Sheaf --- Sheaf cohomology --- Sheaves, Theory of --- Sheaves (Algebraic topology) --- Algebraic topology --- Theory of moduli --- Analytic spaces --- Functions of several complex variables --- Geometry, Algebraic --- Cycles, Algebraic --- Wroński, Józef Maria Hoene-, --- Algebra. --- Geometry, algebraic. --- Algebraic topology. --- Algebraic Geometry. --- Algebraic Topology. --- Topology --- Algebraic geometry --- Geometry --- Mathematics --- Mathematical analysis --- Algebraic geometry.

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Algebraic topology --- Geometry --- landmeetkunde --- topologie (wiskunde)

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Schubert varieties and degeneracy loci have a long history in mathematics, starting from questions about loci of matrices with given ranks. These notes, from a summer school in Thurnau, aim to give an introduction to these topics, and to describe recent progress on these problems. There are interesting interactions with the algebra of symmetric functions and combinatorics, as well as the geometry of flag manifolds and intersection theory and algebraic geometry.

Differential geometry. Global analysis --- Schubert varieties --- Intersection theory --- Vector bundles --- Intersection theory (Mathematics) --- Geometry --- Mathematical Theory --- Mathematics --- Physical Sciences & Mathematics --- Algebraic geometry. --- Combinatorics. --- Group theory. --- Algebraic topology. --- Algebraic Geometry. --- Group Theory and Generalizations. --- Algebraic Topology. --- Topology --- Groups, Theory of --- Substitutions (Mathematics) --- Algebra --- Combinatorics --- Mathematical analysis --- Algebraic geometry --- Schubert varieties. --- Vector bundles. --- Fiber spaces (Mathematics) --- Geometry, Algebraic

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• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

The articles in this volume are devoted to: - moduli of coherent sheaves; - principal bundles and sheaves and their moduli; - new insights into Geometric Invariant Theory; - stacks of shtukas and their compactifications; - algebraic cycles vs. commutative algebra; - Thom polynomials of singularities; - zero schemes of sections of vector bundles. The main purpose is to give "friendly" introductions to the above topics through a series of comprehensive texts starting from a very elementary level and ending with a discussion of current research. In these texts, the reader will find classical results and methods as well as new ones. The book is addressed to researchers and graduate students in algebraic geometry, algebraic topology and singularity theory. Most of the material presented in the volume has not appeared in books before. Contributors: Jean-Marc Drézet, Tomás L. Gómez, Adrian Langer, Piotr Pragacz, Alexander H. W. Schmitt, Vasudevan Srinivas, Ngo Dac Tuan, Andrzej Weber

Algebraic topology --- Geometry --- landmeetkunde --- topologie (wiskunde)