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Ordered algebraic structures --- Noncommutative rings --- Congresses. --- 51 --- -Non-commutative rings --- Associative rings --- Mathematics --- Congresses --- -Mathematics --- 51 Mathematics --- -51 Mathematics --- Non-commutative rings --- Noncommutative rings - Congresses.

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A polarised variety is a modern generalization of the notion of a variety in classical algebraic geometry. It consists of a pair: the algebraic variety itself, together with an ample line bundle on it. Using techniques from abstract algebraic geometry that have been developed over recent decades, Professor Fujita develops classification theories of such pairs using invariants that are polarised higher-dimensional versions of the genus of algebraic curves. The heart of the book is the theory of D-genus and sectional genus developed by the author, but numerous related topics are discussed or surveyed. Proofs are given in full in the central part of the development, but background and technical results are sometimes just sketched when the details are not essential for understanding the key ideas. Readers are assumed to have some background in algebraic geometry, including sheaf cohomology, and for them this work will provide an illustration of the power of modern abstract techniques applied to concrete geometric problems. Thus the book helps the reader not only to understand about classical objects but also modern methods, and so it will be useful not only for experts but also non-specialists and graduate students.

Algebraic varieties --- Classification theory of algebraic varieties --- Classification theory. --- #KVIV:BB --- 512.7 --- 512.7 Algebraic geometry. Commutative rings and algebras --- Algebraic geometry. Commutative rings and algebras --- Classification theory

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Sheaf theory --- Manifolds (Mathematics) --- Algebra, Homological --- Homological algebra --- Algebra, Abstract --- Homology theory --- Geometry, Differential --- Topology --- Cohomology, Sheaf --- Sheaf cohomology --- Sheaves, Theory of --- Sheaves (Algebraic topology) --- Algebraic topology --- Differential geometry. Global analysis --- 512.71 --- 512.71 Commutative rings and algebras. Local theory. Foundations of algebraic geometry --- Commutative rings and algebras. Local theory. Foundations of algebraic geometry --- Topologie algébrique --- Faisceaux, Théorie des --- Algebraic topology. --- Sheaf theory. --- Topologie algébrique --- Faisceaux, Théorie des --- Topologie algebrique --- Geometrie algebrique --- Equations aux derivees partielles sur une variete --- Homologie et cohomologie --- Cohomologie