## Singularities and Computer Algebra

**Author**: Christoph Lossen,Gerhard Pfister

**Publisher:**Cambridge University Press

**ISBN:**9780521683098

**Category:**Computers

**Page:**371

**View:**1690

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A collection of articles giving overviews and open questions in singularities and their computational aspects.

## Singularities in Geometry, Topology, Foliations and Dynamics

*A Celebration of the 60th Birthday of José Seade, Merida, Mexico, December 2014*

**Author**: José Luis Cisneros-Molina,Dũng Tráng Lê,Mutsuo Oka,Jawad Snoussi

**Publisher:**Birkhäuser

**ISBN:**3319393391

**Category:**Mathematics

**Page:**231

**View:**6753

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This book features state-of-the-art research on singularities in geometry, topology, foliations and dynamics and provides an overview of the current state of singularity theory in these settings. Singularity theory is at the crossroad of various branches of mathematics and science in general. In recent years there have been remarkable developments, both in the theory itself and in its relations with other areas. The contributions in this volume originate from the “Workshop on Singularities in Geometry, Topology, Foliations and Dynamics”, held in Merida, Mexico, in December 2014, in celebration of José Seade’s 60th Birthday. It is intended for researchers and graduate students interested in singularity theory and its impact on other fields.

## Zeta Functions in Algebra and Geometry

*Second International Workshop, May 3-7, 2010, Universitat de Les Illes Balears, Palma de Mallorca, Spain*

**Author**: Antonio Campillo

**Publisher:**American Mathematical Soc.

**ISBN:**0821869000

**Category:**Algebraic varieties

**Page:**344

**View:**6955

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The volume contains the proceedings of the ``Second International Workshop on Zeta Functions in Algebra and Geometry'' held May 3-7, 2010 at the Universitat de les Illes Balears, Palma de Mallorca, Spain. Zeta functions can be naturally attached to several mathematical objects, including fields, groups, and algebras. The conference focused on the following topics: arithmetic and geometric aspects of local, topological, and motivic zeta functions, Poincare series of valuations, zeta functions of groups, rings, and representations, prehomogeneous vector spaces and their zeta functions, and height zeta functions. This book is published in cooperation with Real Sociedad Matematica Espanola (RSME).

## Real and Complex Singularities

**Author**: M. Manoel,M. C. Romero Fuster,C. T. C. Wall

**Publisher:**Cambridge University Press

**ISBN:**1139489917

**Category:**Mathematics

**Page:**N.A

**View:**6988

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The biennial meetings at São Carlos have helped create a worldwide community of experts and young researchers working on singularity theory, with a special focus on applications to a wide variety of topics in both pure and applied mathematics. The tenth meeting, celebrating the 60th birthdays of Terence Gaffney and Maria Aparecida Soares Ruas, was a special occasion attracting the best known names in the area. This volume contains contributions by the attendees, including three articles written or co-authored by Gaffney himself, and survey articles on the existence of Milnor fibrations, global classifications and graphs, pairs of foliations on surfaces, and Gaffney's work on equisingularity.

## A Study of Singularities on Rational Curves Via Syzygies

**Author**: David A. Cox,Andrew R. Kustin,Claudia Polini,Bernd Ulrich

**Publisher:**American Mathematical Soc.

**ISBN:**0821887432

**Category:**Mathematics

**Page:**116

**View:**6818

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Consider a rational projective curve $\mathcal{C}$ of degree $d$ over an algebraically closed field $\pmb k$. There are $n$ homogeneous forms $g_{1},\dots, g_{n}$ of degree $d$ in $B=\pmb k[x, y]$ which parameterize $\mathcal{C}$ in a birational, base point free, manner. The authors study the singularities of $\mathcal{C}$ by studying a Hilbert-Burch matrix $\varphi$ for the row vector $[g_{1},\dots, g_{n}]$. In the ``General Lemma'' the authors use the generalized row ideals of $\varphi$ to identify the singular points on $\mathcal{C}$, their multiplicities, the number of branches at each singular point, and the multiplicity of each branch. Let $p$ be a singular point on the parameterized planar curve $\mathcal{C}$ which corresponds to a generalized zero of $\varphi$. In the `'triple Lemma'' the authors give a matrix $\varphi'$ whose maximal minors parameterize the closure, in $\mathbb{P}^{2}$, of the blow-up at $p$ of $\mathcal{C}$ in a neighborhood of $p$. The authors apply the General Lemma to $\varphi'$ in order to learn about the singularities of $\mathcal{C}$ in the first neighborhood of $p$. If $\mathcal{C}$ has even degree $d=2c$ and the multiplicity of $\mathcal{C}$ at $p$ is equal to $c$, then he applies the Triple Lemma again to learn about the singularities of $\mathcal{C}$ in the second neighborhood of $p$. Consider rational plane curves $\mathcal{C}$ of even degree $d=2c$. The authors classify curves according to the configuration of multiplicity $c$ singularities on or infinitely near $\mathcal{C}$. There are $7$ possible configurations of such singularities. They classify the Hilbert-Burch matrix which corresponds to each configuration. The study of multiplicity $c$ singularities on, or infinitely near, a fixed rational plane curve $\mathcal{C}$ of degree $2c$ is equivalent to the study of the scheme of generalized zeros of the fixed balanced Hilbert-Burch matrix $\varphi$ for a parameterization of $\mathcal{C}$.

## The British National Bibliography

**Author**: Arthur James Wells

**Publisher:**N.A

**ISBN:**N.A

**Category:**English literature

**Page:**N.A

**View:**8172

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## Computer Algebra and Differential Equations

**Author**: Evelyne Tournier

**Publisher:**Cambridge University Press

**ISBN:**9780521447577

**Category:**Mathematics

**Page:**259

**View:**6900

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Selected papers from the Computer Algebra and Differential Equations meeting held in France in June 1992.

## London Mathematical Society lecture note series

**Author**: Boris I. Botvinnik

**Publisher:**N.A

**ISBN:**N.A

**Category:**

**Page:**N.A

**View:**8554

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## Singularity Theory

*Proceedings of the European Singularities Conference, August 1996, Liverpool and Dedicated to C.T.C. Wall on the Occasion of His 60th Birthday*

**Author**: Charles Terence Clegg Wall,D. Mond

**Publisher:**Cambridge University Press

**ISBN:**9780521658881

**Category:**Computers

**Page:**440

**View:**7720

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An up-to-date survey of research in singularity theory.

## London Mathematical Society lecture note series

**Author**: Michael Sh Braverman

**Publisher:**N.A

**ISBN:**N.A

**Category:**

**Page:**N.A

**View:**1899

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## London Mathematical Society lecture note series

**Author**: Manfred Stoll

**Publisher:**N.A

**ISBN:**N.A

**Category:**

**Page:**N.A

**View:**3608

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## London Mathematical Society lecture note series

**Author**: Akihiko Yukie

**Publisher:**N.A

**ISBN:**N.A

**Category:**

**Page:**N.A

**View:**872

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## London Mathematical Society lecture note series

**Author**: Olaf Manz,Thomas R. Wolf

**Publisher:**N.A

**ISBN:**N.A

**Category:**

**Page:**N.A

**View:**3579

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## London Mathematical Society lecture note series

**Author**: William J. Harvey,C. MacLachlan

**Publisher:**N.A

**ISBN:**N.A

**Category:**

**Page:**N.A

**View:**6767

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## London Mathematical Society lecture note series

**Author**: Alain Grigis,Johannes Sjöstrand

**Publisher:**N.A

**ISBN:**N.A

**Category:**

**Page:**N.A

**View:**4195

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## London Mathematical Society lecture note series

**Author**: Jiří Adámek (Ing.)

**Publisher:**N.A

**ISBN:**N.A

**Category:**

**Page:**N.A

**View:**530

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## London Mathematical Society lecture note series

**Author**: Dietmar Salamon

**Publisher:**N.A

**ISBN:**N.A

**Category:**

**Page:**N.A

**View:**2899

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## London Mathematical Society lecture note series

**Author**: Mark Pollicott

**Publisher:**N.A

**ISBN:**N.A

**Category:**

**Page:**N.A

**View:**5883

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## London Mathematical Society lecture note series

**Author**: Graham A. Niblo,Martin A. Roller

**Publisher:**N.A

**ISBN:**N.A

**Category:**

**Page:**N.A

**View:**559

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## London Mathematical Society lecture note series

**Author**: E. Tournier

**Publisher:**N.A

**ISBN:**N.A

**Category:**

**Page:**N.A

**View:**1915

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