Title: Commutative algebra and its connections to geometry
Description: This volume contains papers based on presentations given at the Pan-American Advanced Studies Institute (PASI) on commutative algebra and its connections to geometry, which was held August 3-14, 2009, at the Universidade Federal de Pernambuco in Olinda, Brazil. The main goal of the program was to detail recent developments in commutative algebra and interactions with such areas as algebraic geometry, combinatorics and computer algebra. The articles in this volume concentrate on topics central to modern commutative algebra: the homological conjectures, problems in positive and mixed characteristic, tight closure and its interaction with birational geometry, integral dependence and blowup algebras, equisingularity theory, Hilbert functions and multiplicities, combinatorial commutative algebra, Grobner bases and computational algebra.
Subjects: Commutative algebra -- Homological methods -- Syzygies, resolutions, complexes, Algebraic geometry -- Surfaces and higher-dimensional varieties -- Vector bundles on surfaces and higher-dimensional varieties, and their moduli, Homological Algebra, Algebraic Geometry, Commutative algebra -- Homological methods -- Homological functors on modules (Tor, Ext, etc.)., Algebraic geometry -- Special varieties -- Determinantal varieties, Algebraic geometry -- Cycles and subschemes -- Parametrization (Chow and Hilbert schemes), Commutative algebra -- Theory of modules and ideals -- Linkage, complete intersections and determinantal ideals, Algebraic geometry -- Projective and enumerative geometry -- Projective techniques, Congresses, Combinatorial group theory, Commutative algebra -- Homological methods -- Hilbert-Samuel and Hilbert-Kunz functions; PoincarÃ© series, Combinatorics -- Graph theory -- Applications, Syzygies, resolutions, complexes, Combinatorics, Vector bundles on surfaces and higher-dimensional varieties, and their moduli, Linkage, complete intersections and determinantal ideals, Cycles and subschemes, Theory of modules and ideals, Projective and enumerative geometry, Surfaces and higher-dimensional varieties, Projective techniques, Graph theory, Hilbert-Samuel and Hilbert-Kunz functions; PoincaräAÃ series, Parametrization (Chow and Hilbert schemes), Commutative algebra, Applications, Homological methods, Homological methods x Homological functors on modules (Tor, Ext, etc.), Special varieties, Determinantal varieties, Algebra, homological, Geometry, algebraic, Combinatorial analysis, Commutative algebra -- Homological methods -- Homological functors on modules (Tor, Ext, etc.)