Introduction to Singularities
Autor Shihoko Ishiien Limba Engleză Paperback – 25 dec 2018
Algebraic geometry is said to have originated in the seventeenth century with the famous work Discours de la méthode pour bien conduire sa raison, et chercher la vérité dans les sciences by Descartes. In that book he introduced coordinates to the study of geometry. After its publication, research on algebraic varieties developed steadily. Many beautiful results emerged in mathematicians’ works. First, mostly non-singular varieties were studied. In the past three decades, however, it has become clear that singularities are necessary for us to have a good description of the framework of varieties. For example, it is impossible to formulate minimal model theory for higher-dimensional cases without singularities. A remarkable fact is that the study of singularities is developing and people are beginning to see that singularities are interesting and can be handled by human beings. This bookis a handy introduction to singularities for anyone interested in singularities. The focus is on an isolated singularity in an algebraic variety. After preparation of varieties, sheaves, and homological algebra, some known results about 2-dimensional isolated singularities are introduced. Then a classification of higher-dimensional isolated singularities is shown according to plurigenera and the behavior of singularities under a deformation is studied. In the second edition, brief descriptions about recent remarkable developments of the researches are added as the last chapter.
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Paperback (2) | 427.84 lei 6-8 săpt. | |
Springer – 25 dec 2018 | 427.84 lei 6-8 săpt. | |
Springer – 23 aug 2016 | 458.35 lei 6-8 săpt. | |
Hardback (2) | 375.76 lei 39-44 zile | |
Springer – 2 dec 2014 | 375.76 lei 39-44 zile | |
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Specificații
ISBN-13: 9784431568711
ISBN-10: 4431568719
Pagini: 236
Ilustrații: X, 236 p. 4 illus.
Dimensiuni: 155 x 235 x 13 mm
Greutate: 0.35 kg
Ediția:Softcover reprint of the original 2nd ed. 2018
Editura: Springer
Colecția Springer
Locul publicării:Tokyo, Japan
ISBN-10: 4431568719
Pagini: 236
Ilustrații: X, 236 p. 4 illus.
Dimensiuni: 155 x 235 x 13 mm
Greutate: 0.35 kg
Ediția:Softcover reprint of the original 2nd ed. 2018
Editura: Springer
Colecția Springer
Locul publicării:Tokyo, Japan
Cuprins
1. Sheaves, algebraic varieties and analytic spaces.- 2. Homological algebra and duality.- 3. Singularities, algebraization and resolutions of singularities.- 4. Divisors on a variety and the corresponding sheaves.- 5. Differential forms around the singularities.- 6. Two dimensional singularities.- 7. Higher dimensional singularities.- 8. Deformations of singularities.
Notă biografică
Shihoko Ishii is a professor emeritus at the University of Tokyo and a professor at the Tokyo Woman's Christian University.
Textul de pe ultima copertă
This book is an introduction to singularities for graduate students and researchers.
Algebraic geometry is said to have originated in the seventeenth century with the famous workDiscours de la méthode pour bien conduire sa raison, et chercher la vérité dans les sciences by Descartes. In that book he introduced coordinates to the study of geometry. After its publication, research on algebraic varieties developed steadily. Many beautiful results emerged in mathematicians’ works. First, mostly non-singular varieties were studied. In the past three decades, however, it has become clear that singularities are necessary for us to have a good description of the framework of varieties. For example, it is impossible to formulate minimal model theory for higher-dimensional cases without singularities. A remarkable fact is that the study of singularities is developing and people are beginning to see that singularities are interesting and can be handled by human beings. This book is a handy introduction to singularities for anyone interested in singularities. The focus is on an isolated singularity in an algebraic variety. After preparation of varieties, sheaves, and homological algebra, some known results about 2-dimensional isolated singularities are introduced. Then a classification of higher-dimensional isolated singularities is shown according to plurigenera and the behavior of singularities under a deformation is studied. In the second edition, brief descriptions about recent remarkable developments of the researches are added as the last chapter.
Algebraic geometry is said to have originated in the seventeenth century with the famous workDiscours de la méthode pour bien conduire sa raison, et chercher la vérité dans les sciences by Descartes. In that book he introduced coordinates to the study of geometry. After its publication, research on algebraic varieties developed steadily. Many beautiful results emerged in mathematicians’ works. First, mostly non-singular varieties were studied. In the past three decades, however, it has become clear that singularities are necessary for us to have a good description of the framework of varieties. For example, it is impossible to formulate minimal model theory for higher-dimensional cases without singularities. A remarkable fact is that the study of singularities is developing and people are beginning to see that singularities are interesting and can be handled by human beings. This book is a handy introduction to singularities for anyone interested in singularities. The focus is on an isolated singularity in an algebraic variety. After preparation of varieties, sheaves, and homological algebra, some known results about 2-dimensional isolated singularities are introduced. Then a classification of higher-dimensional isolated singularities is shown according to plurigenera and the behavior of singularities under a deformation is studied. In the second edition, brief descriptions about recent remarkable developments of the researches are added as the last chapter.
Caracteristici
Presents a unique combination of birational geometry, traditional local aspects of singularities, and new developments in research on singularities Shows concise introductions of tools for study of singularities such as homological algebra, spectral sequence, toric varieties, and Hodge theory, which are also useful for study of other subjects in algebra and algebraic geometry Describes briefly the recent dramatic developments of the three directions in research on singularities
Recenzii
“This
book
presents
some
results
of
the
study
of
singularities
within
the
field
of
algebraic
geometry.
…
The
text
is
clear
and
well
written
and
it
is
accessible
to
non-expert
readers.
…
the
author
defines
all
the
concepts
and
the
results
are
either
proved
or
a
reference
is
provided.
This
makes
the
book
self-contained
in
a
broad
sense.
It
is
a
useful
volume
both
for
readers
studying
singular
varieties
for
the
first
time
and
for
experts
on
classification
of
singularities.”
(Santiago
Encinas,
Mathematical
Reviews,
August,
2015)