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An overview of developments in the past 15 years of adjunction theory, the study of the interplay between the intrinsic geometry of a projective variety and the geometry connected with some embedding of the variety into a projective space. Topics include consequences of positivity, the Hilbert schem

Adjunction theory. --- Algebraic varieties. --- Embeddings (Mathematics) --- Projective spaces. --- Embeddings (Mathematics). --- Adjunction theory --- Algebraic varieties --- Projective spaces --- 512.7 --- 512.7 Algebraic geometry. Commutative rings and algebras --- Algebraic geometry. Commutative rings and algebras --- Spaces, Projective --- Geometry, Projective --- Imbeddings (Mathematics) --- Geometry, Algebraic --- Immersions (Mathematics) --- Varieties, Algebraic --- Linear algebraic groups

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In the last decade, there has been a burgeoning of activity in the design and implementation of algorithms for algebraic geometric compuation. Some of these algorithms were originally designed for abstract algebraic geometry, but now are of interest for use in applications and some of these algorithms were originally designed for applications, but now are of interest for use in abstract algebraic geometry. The workshop on Algorithms in Algebraic Geometry that was held in the framework of the IMA Annual Program Year in Applications of Algebraic Geometry by the Institute for Mathematics and Its Applications on September 18-22, 2006 at the University of Minnesota is one tangible indication of the interest. One hundred ten participants from eleven countries and twenty states came to listen to the many talks; discuss mathematics; and pursue collaborative work on the many faceted problems and the algorithms, both symbolic and numberic, that illuminate them. This volume of articles captures some of the spirit of the IMA workshop.

Mathematics. --- Algebraic Geometry. --- Algorithms. --- Applications of Mathematics. --- Geometry, algebraic. --- Mathématiques --- Algorithmes --- Algorithms -- Congresses. --- Geometry, Algebraic -- Data processing -- Congresses. --- Geometry, Algebraic -- Data processing. --- Geometry, Algebraic --- Algorithms --- Geometry --- Mathematics --- Physical Sciences & Mathematics --- Data processing --- Algebraic geometry --- Algebraic geometry. --- Applied mathematics. --- Engineering mathematics. --- Math --- Science --- Algorism --- Algebra --- Arithmetic --- Foundations --- Engineering --- Engineering analysis --- Mathematical analysis

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Geometry, Algebraic