| Description |
1 online resource (xv, 345 pages) : illustrations. |
| Physical Medium |
polychrome |
| Description |
text file |
| Series |
London Mathematical Society lecture note series ; 276
|
|
London Mathematical Society lecture note series ; 276.
|
| Bibliography |
Includes bibliographical references (pages 333-338) and index. |
| Contents |
Projective spaces -- Power series -- Surfaces, local coordinates -- Morphisms -- Local rings -- Tangent and cotangent spaces -- Curves -- Germs of curves -- Multiplicity and tangent cone -- Smooth germs -- Examples of singular germs -- Newton--Puiseux algorithm -- Newton polygon -- Fractionary power series -- Search for y-roots of f(x, y) -- Newton-Puiseux algorithm -- Puiseux theorem -- Separation of y-roots -- Case of convergent series -- Algebraic properties of C{x, y} -- First local properties of plane curves -- Branches of a germ -- Puiseux series of a germ -- Points on curves around O -- Local rings of germs -- Parameterizing branches -- Intersection multiplicity -- Pencils and linear systems -- Infinitely near points -- Blowing up -- Transforming curves and germs -- Infinitely near points -- Enriques' definition of infinitely near points -- Proximity -- Free and satellite points -- Resolution of singularities -- Equisingularity -- Enriques diagrams -- Ring in the first neighbourhood -- Rings in the successive neighbourhoods -- Artin theorem for plane curves -- Virtual multiplicities -- Curves through a weighted cluster -- When virtual multiplicities are effective -- Blowing up all points in a cluster -- Exceptional divisors and dual graphs -- Totla transform of a curve -- Unloading -- Number of conditions -- Adjoint germs and curves -- Noether's Af + B[phi] theorem -- Analysis of branches -- Characteristic exponents -- First characteristic exponent. |
| Summary |
Comprehensive and self-contained exposition of singularities of plane curves, including new, previously unpublished results. |
| Local Note |
eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America |
| Subject |
Curves, Plane.
|
|
Curves, Plane. |
|
Singularities (Mathematics)
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|
Singularities (Mathematics) |
| Genre/Form |
Electronic books.
|
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Electronic books.
|
| Other Form: |
Print version: Casas-Alvero, E. (Eduardo), 1948- Singularities of plane curves. Cambridge ; New York : Cambridge University Press, 2000 0521789591 (DLC) 00027671 (OCoLC)43607435 |
| ISBN |
9781107363113 (electronic book) |
|
110736311X (electronic book) |
|
9780511569326 (e-book) |
|
0511569327 (e-book) |
|
9781107368026 |
|
1107368022 |
|
0521789591 |
|
9780521789592 |
|
