The course was designed to go beyond the mathematics of resolving singularities of algebraic varieties and represent a step in the career of participants by teaching them how to grasp and incorporate the main features of a complicated theory, to evaluate and combine the many ideas involved in its proofs, and to develop an overall picture of what mathematics can be good for with respect to intellectual, cultural, and personal development. Nine lectures consider such topics as blowups and resolution, a simplified game for resolving singularities, resolving toric varieties, introduction to the idealistic filtration program with an emphasis on the radical saturation, and higher Semple-Nash blowups and F-blowups. Annotation ©2015 Ringgold, Inc., Portland, OR (protoview.com)
| Preface |
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ix | |
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1 | (80) |
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On the Behavior of the Multiplicity on Schemes: Stratification and Blow Ups |
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81 | (128) |
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A Simplified Game for Resolution of Singularities |
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209 | (16) |
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Resolution of Singularities in Characteristic P and Monomialization |
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225 | (14) |
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Resolution of Toric Varieties |
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239 | (30) |
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Desingularization in Computational Applications and Experiments |
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269 | (16) |
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Introduction to the Idealistic Filtration Program with Emphasis on the Radical Saturation |
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285 | (34) |
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Algebraic Approaches to FlipIt |
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319 | (8) |
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Higher Semple-Nash Blowups and F-Blowups |
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327 | |
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David Ellwood, Harvard University, Cambridge, MA, USA.
Herwig Hauser, Universtitat Wien, Vienna, Austria.
Shigefumi Mori, RIMS, Kyoto University, Japan.
Josef Schicho, Austrian Academy of Sciences, Linz, Austria.
