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"Algebraic Geometry often seems very abstract, but in fact it is full of concrete examples and problems. This side of the subject can be approached through the equations of a variety, and the syzygies of these equations are a necessary part of the study. This book is the first textbook-level account of basic examples and techniques in this area. It illustrates the use of syzygies in many concrete geometric considerations, from interpolation to the study of canonical curves. The text has served as a basis for graduate courses by the author at Berkeley, Brandeis, and in Paris. It is also suitable for self-study by a reader who knows a little commutative algebra and algebraic geometry already. As an aid to the reader, the appendices provide summaries of local cohomology and commutative algebra, tying together examples and major results from a wide range of topics."--Publisher's website.

Commutative algebra. --- Geometry, Algebraic. --- Syzygies (Mathematics). --- Commutative algebra --- Geometry, Algebraic --- Syzygies (Mathematics) --- Syzygy theory (Mathematics) --- Categories (Mathematics) --- Rings (Algebra) --- Algebraic geometry --- Geometry --- Algebra

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"A collection of critical and creative essays exploring pataphysics, a late nineteenth-century French absurdist precursor to Dadaism, surrealism, and the Theater of the Absurd. Reveals how pataphysics has been a platform and medium for persistent intellectual, poetic, conceptual, and artistic experimentation for over a century"--

Pataphysics --- History. --- Absolute. --- Alfred Jarry. --- Anomaly. --- Antimony. --- Canadian ”Pataphysics. --- Clinamen. --- Faustroll. --- Imaginary Solutions. --- Modernism. --- Oulipo. --- Pataphor. --- Pataphysics. --- Philosophy. --- Postmodernism. --- Science. --- Sieve. --- Syzygy. --- Ubu Roi.

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The aim of this book, which was originally published in 1985, is to cover from first principles the theory of Syzygies, building up from a discussion of the basic commutative algebra to such results as the authors' proof of the Syzygy Theorem. In the last three chapters applications of the theory to commutative algebra and algebraic geometry are given.

Syzygies (Mathematics) --- Rings (Algebra) --- Vector bundles. --- Fiber spaces (Mathematics) --- Algebraic rings --- Ring theory --- Algebraic fields --- Syzygy theory (Mathematics) --- Categories (Mathematics) --- Vector bundles --- 512.55 --- 512.55 Rings and modules --- Rings and modules

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This book introduces a theory of higher matrix factorizations for regular sequences and uses it to describe the minimal free resolutions of high syzygy modules over complete intersections. Such resolutions have attracted attention ever since the elegant construction of the minimal free resolution of the residue field by Tate in 1957. The theory extends the theory of matrix factorizations of a non-zero divisor, initiated by Eisenbud in 1980, which yields a description of the eventual structure of minimal free resolutions over a hypersurface ring. Matrix factorizations have had many other uses in a wide range of mathematical fields, from singularity theory to mathematical physics.

Algebra --- Mathematics --- Physical Sciences & Mathematics --- Mathematics. --- Algebraic geometry. --- Category theory (Mathematics). --- Homological algebra. --- Commutative algebra. --- Commutative rings. --- Physics. --- Commutative Rings and Algebras. --- Algebraic Geometry. --- Category Theory, Homological Algebra. --- Theoretical, Mathematical and Computational Physics. --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Rings (Algebra) --- Homological algebra --- Algebra, Abstract --- Homology theory --- Category theory (Mathematics) --- Algebra, Homological --- Algebra, Universal --- Group theory --- Logic, Symbolic and mathematical --- Topology --- Functor theory --- Algebraic geometry --- Geometry --- Math --- Science --- Algebra. --- Geometry, algebraic. --- Mathematical analysis --- Syzygies (Mathematics) --- Resolvents (Mathematics) --- Geometry, Algebraic. --- Syzygy theory (Mathematics) --- Categories (Mathematics) --- Resolvent of an operator --- Matrices --- Operator theory --- Mathematical physics. --- Physical mathematics --- Physics --- Algebra, Homological.

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This book contains a collection of twelve papers that reflect the state of the art of nonlinear differential equations in modern geometrical theory. It comprises miscellaneous topics of the local and nonlocal geometry of differential equations and the applications of the corresponding methods in hydrodynamics, symplectic geometry, optimal investment theory, etc. The contents will be useful for all the readers whose professional interests are related to nonlinear PDEs and differential geometry, both in theoretical and applied aspects.

Research & information: general --- Mathematics & science --- adjoint-symmetry --- one-form --- symmetry --- vector field --- geometrical formulation --- nonlocal conservation laws --- differential coverings --- polynomial and rational invariants --- syzygy --- free resolution --- discretization --- differential invariants --- invariant derivations --- symplectic --- contact spaces --- Euler equations --- shockwaves --- phase transitions --- symmetries --- integrable systems --- Darboux-Bäcklund transformation --- isothermic immersions --- Spin groups --- Clifford algebras --- Euler equation --- quotient equation --- contact symmetry --- optimal investment theory --- linearization --- exact solutions --- Korteweg–de Vries–Burgers equation --- cylindrical and spherical waves --- saw-tooth solutions --- periodic boundary conditions --- head shock wave --- Navier–Stokes equations --- media with inner structures --- plane molecules --- water --- Levi–Civita connections --- Lagrangian curve flows --- KdV type hierarchies --- Darboux transforms --- Sturm–Liouville --- clamped --- hinged boundary condition --- spectral collocation --- Chebfun --- chebop --- eigenpairs --- preconditioning --- drift --- error control --- adjoint-symmetry --- one-form --- symmetry --- vector field --- geometrical formulation --- nonlocal conservation laws --- differential coverings --- polynomial and rational invariants --- syzygy --- free resolution --- discretization --- differential invariants --- invariant derivations --- symplectic --- contact spaces --- Euler equations --- shockwaves --- phase transitions --- symmetries --- integrable systems --- Darboux-Bäcklund transformation --- isothermic immersions --- Spin groups --- Clifford algebras --- Euler equation --- quotient equation --- contact symmetry --- optimal investment theory --- linearization --- exact solutions --- Korteweg–de Vries–Burgers equation --- cylindrical and spherical waves --- saw-tooth solutions --- periodic boundary conditions --- head shock wave --- Navier–Stokes equations --- media with inner structures --- plane molecules --- water --- Levi–Civita connections --- Lagrangian curve flows --- KdV type hierarchies --- Darboux transforms --- Sturm–Liouville --- clamped --- hinged boundary condition --- spectral collocation --- Chebfun --- chebop --- eigenpairs --- preconditioning --- drift --- error control