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The basic problem of deformation theory in algebraic geometry
involves watching a small deformation of one member of a family of
objects, such as varieties, or subschemes in a fixed space, or
vector bundles on a fixed scheme. In this new book, Robin
Hartshorne studies first what happens over small infinitesimal
deformations, and then gradually builds up to more global
situations, using methods pioneered by Kodaira and Spencer in the
complex analytic case, and adapted and expanded in algebraic
geometry by Grothendieck.
The author includes numerous exercises, as well as important
examples illustrating various aspects of the theory. This text is
based on a graduate course taught by the author at the University
of California, Berkeley.
This book offers a unique opportunity to understand the essence of one of the great thinkers of western civilization. A guided reading of Euclid's Elements leads to a critical discussion and rigorous modern treatment of Euclid's geometry and its more recent descendants, with complete proofs. Topics include the introduction of coordinates, the theory of area, geometrical constructions and finite field extensions, history of the parallel postulate, the various non-Euclidean geometries, and the regular and semi-regular polyhedra. The text is intended for junior- to senior-level mathematics majors. Robin Hartshorne is a professor of mathematics at the University of California at Berkeley, and is the author of Foundations of Projective Geometry (Benjamin, 1967) and Algebraic Geometry (Springer, 1977).
Robin Hartshorne studied algebraic geometry with Oscar Zariski and David Mumford at Harvard, and with J.-P. Serre and A. Grothendieck in Paris. After receiving his Ph.D. from Princeton in 1963, Hartshorne became a Junior Fellow at Harvard, then taught there for several years. In 1972 he moved to California where he is now Professor at the University of California at Berkeley. He is the author of "Residues and Duality" (1966), "Foundations of Projective Geometry (1968), "Ample Subvarieties of Algebraic Varieties" (1970), and numerous research titles. His current research interest is the geometry of projective varieties and vector bundles. He has been a visiting professor at the College de France and at Kyoto University, where he gave lectures in French and in Japanese, respectively. Professor Hartshorne is married to Edie Churchill, educator and psychotherapist, and has two sons. He has travelled widely, speaks several foreign languages, and is an experienced mountain climber. He is also an accomplished amateur musician: he has played the flute for many years, and during his last visit to Kyoto he began studying the shakuhachi.
The basic problem of deformation theory in algebraic geometry
involves watching a small deformation of one member of a family of
objects, such as varieties, or subschemes in a fixed space, or
vector bundles on a fixed scheme. In this new book, Robin
Hartshorne studies first what happens over small infinitesimal
deformations, and then gradually builds up to more global
situations, using methods pioneered by Kodaira and Spencer in the
complex analytic case, and adapted and expanded in algebraic
geometry by Grothendieck.
The author includes numerous exercises, as well as important
examples illustrating various aspects of the theory. This text is
based on a graduate course taught by the author at the University
of California, Berkeley.
This book offers a unique opportunity to understand the essence of
one of the great thinkers of western civilization. A guided reading
of Euclid's Elements leads to a critical discussion and rigorous
modern treatment of Euclid's geometry and its more recent
descendants, with complete proofs. Topics include the introduction
of coordinates, the theory of area, geometrical constructions and
finite field extensions, history of the parallel postulate, the
various non-Euclidean geometries, and the regular and semi-regular
polyhedra. The text is intended for junior- to senior-level
mathematics majors. Robin Hartshorne is a professor of mathematics
at the University of California at Berkeley, and is the author of
Foundations of Projective Geometry (Benjamin, 1967) and Algebraic
Geometry (Springer, 1977).
This small book, translated into English for the first time, has
long been a unique place to find classical results from geometry,
such as Pythagoras' theorem, the nine-point circle, Morley's
triangle, and many other subjects. In addition, this book contains
recent, geometric theorems which have been obtained over the past
years. There are 27 independent chapters on a wide range of topics
in elementary plane Euclidean geometry, at a level just beyond what
is usually taught in a good high school or college geometry course.
The selection of topics is intelligent, varied, and stimulating,
and the author provides many thought-provoking ideas.
An introduction to abstract algebraic geometry, with the only
prerequisites being results from commutative algebra, which are
stated as needed, and some elementary topology. More than 400
exercises distributed throughout the book offer specific examples
as well as more specialised topics not treated in the main text,
while three appendices present brief accounts of some areas of
current research. This book can thus be used as textbook for an
introductory course in algebraic geometry following a basic
graduate course in algebra.
Robin Hartshorne studied algebraic geometry with Oscar Zariski and
David Mumford at Harvard, and with J.-P. Serre and A. Grothendieck
in Paris. He is the author of "Residues and Duality," "Foundations
of Projective Geometry," "Ample Subvarieties of Algebraic
Varieties," and numerous research titles.
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