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The aim of this monograph is to introduce the reader to modern
methods of projective geometry involving certain techniques of
formal geometry. Some of these methods are illustrated in the first
part through the proofs of a number of results of a rather
classical flavor, involving in a crucial way the first
infinitesimal neighbourhood of a given subvariety in an ambient
variety. Motivated by the first part, in the second formal
functions on the formal completion X/Y of X along a closed
subvariety Y are studied, particularly the extension problem of
formal functions to rational functions.
The main aim of this book is to present a completely algebraic approach to the Enriques classification of smooth projective surfaces defined over an algebraically closed field of arbitrary characteristic. This algebraic approach is one of the novelties of this book among the other modern textbooks devoted to this subject. Two chapters on surface singularities are also included. The book can be useful as a textbook for a graduate course on surfaces, for researchers or graduate students in algebraic geometry, as well as those mathematicians working in algebraic geometry or related fields.
The aim of this monograph is to introduce the reader to modern
methods of projective geometry involving certain techniques of
formal geometry. Some of these methods are illustrated in the first
part through the proofs of a number of results of a rather
classical flavor, involving in a crucial way the first
infinitesimal neighbourhood of a given subvariety in an ambient
variety. Motivated by the first part, in the second formal
functions on the formal completion X/Y of X along a closed
subvariety Y are studied, particularly the extension problem of
formal functions to rational functions.
The main aim of this book is to present a completely algebraic approach to the Enriques¿ classification of smooth projective surfaces defined over an algebraically closed field of arbitrary characteristic. This algebraic approach is one of the novelties of this book among the other modern textbooks devoted to this subject. Two chapters on surface singularities are also included. The book can be useful as a textbook for a graduate course on surfaces, for researchers or graduate students in algebraic geometry, as well as those mathematicians working in algebraic geometry or related fields.
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