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Resolution of Curve and Surface Singularities in Characteristic Zero

Resolution of Curve and Surface Singularities in Characteristic Zero
Author: K. Kiyek
Publisher: Springer Science & Business Media
Total Pages: 506
Release: 2012-09-11
Genre: Mathematics
ISBN: 1402020295

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The Curves The Point of View of Max Noether Probably the oldest references to the problem of resolution of singularities are found in Max Noether's works on plane curves [cf. [148], [149]]. And probably the origin of the problem was to have a formula to compute the genus of a plane curve. The genus is the most useful birational invariant of a curve in classical projective geometry. It was long known that, for a plane curve of degree n having l m ordinary singular points with respective multiplicities ri, i E {1, . . . , m}, the genus p of the curve is given by the formula = (n - l)(n - 2) _ ~ "r. (r. _ 1) P 2 2 L. . ,. •• . Of course, the problem now arises: how to compute the genus of a plane curve having some non-ordinary singularities. This leads to the natural question: can we birationally transform any (singular) plane curve into another one having only ordinary singularities? The answer is positive. Let us give a flavor (without proofs) 2 on how Noether did it • To solve the problem, it is enough to consider a special kind of Cremona trans formations, namely quadratic transformations of the projective plane. Let ~ be a linear system of conics with three non-collinear base points r = {Ao, AI, A }, 2 and take a projective frame of the type {Ao, AI, A ; U}.


Yvain

Yvain
Author: Chretien de Troyes
Publisher: Yale University Press
Total Pages: 244
Release: 1987-09-10
Genre: Poetry
ISBN: 0300038380

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A twelfth-century poem by the creator of the Arthurian romance describes the courageous exploits and triumphs of a brave lord who tries to win back his deserted wife's love


Annual Review of Information Science and Technology

Annual Review of Information Science and Technology
Author: Information Today Inc
Publisher: Information Today, Inc.
Total Pages: 632
Release: 2005-10
Genre: Computers
ISBN: 9781573872423

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ARIST, published annually since 1966, is a landmark publication within the information science community. It surveys the landscape of information science and technology, providing an analytical, authoritative, and accessible overview of recent trends and significant developments. The range of topics varies considerably, reflecting the dynamism of the discipline and the diversity of theoretical and applied perspectives. While ARIST continues to cover key topics associated with "classical" information science (e.g., bibliometrics, information retrieval), editor Blaise Cronin is selectively expanding its footprint in an effort to connect information science more tightly with cognate academic and professional communities. Contents of Volume 40 (2006): SECTION I: Information and Society Chapter 1: The Micro- and Macroeconomics of Information, Sandra Braman Chapter 2: The Geographies of the Internet, Matthew Zook Chapter 3: Open Access, M. Carl Drott SECTION II: Technologies and Systems Chapter 4: TREC: An Overview, Donna K. Harman and Ellen M. Voorhees Chapter 5: Semantic Relations in Information Science, Christopher S. G. Khoo and Jin-Cheon Na Chapter 6: Intelligence and Security Informatics, Hsinchun Chen and Jennifer Xu SECTION III: Information Needs and Use Chapter 7: Information Behavior, Donald O. Case Chapter 8: Collaborative Information Seeking and Retrieval, Jonathan Foster Chapter 9: Information Failures in Health Care, Anu MacIntosh-Murray and Chun Wei Choo Chapter 10: Workplace Studies and Technological Change, Angela Cora Garcia, Mark E. Dawes, Mary Lou Kohne, Felicia Miller, and Stephan F. Groschwitz SECTION IV: Theoretical Perspectives Chapter 11: Information History, Alistair Black Chapter 12: Social Epistemology and Information Science, Don Fallis Chapter 13: Formal Concept Analysis in Information Science, Uta Priss.


Content Critical

Content Critical
Author: Gerry McGovern
Publisher: FT Press
Total Pages: 264
Release: 2002
Genre: Business & Economics
ISBN: 9780273656043

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The web's made everyone a publisher, so what's going to make people read what YOU write? The answer is high-quality, well-written, reader-focused, compelling content. This is the book that explores what "killer content" actually is, and shows how to create it for yourself.