Algebraic Geometry and its Applications will be of interest not only to mathematicians but also to computer scientists working on visualization and related topics. The book is based on 32 invited papers presented at a conference in honor of Shreeram Abhyankar's 60th birthday, which was held in June 1990 at Purdue University and attended by many renowned mathematicians (field medalists), computer scientists and engineers. The keynote paper is by G. Birkhoff; other contributors include such leading names in algebraic geometry as R. Hartshorne, J. Heintz, J.I. Igusa, D. Lazard, D. Mumford, and J.-P. Serre.…mehr
Algebraic Geometry and its Applications will be of interest not only to mathematicians but also to computer scientists working on visualization and related topics. The book is based on 32 invited papers presented at a conference in honor of Shreeram Abhyankar's 60th birthday, which was held in June 1990 at Purdue University and attended by many renowned mathematicians (field medalists), computer scientists and engineers. The keynote paper is by G. Birkhoff; other contributors include such leading names in algebraic geometry as R. Hartshorne, J. Heintz, J.I. Igusa, D. Lazard, D. Mumford, and J.-P. Serre.
I Past, Present, and Future.- Mathematics and India.- II Algebraic Curves.- 2 Square-root Parametrization of Plane Curves.- 3 A Letter as an Appendix to the Square-Root Parameterization Paper Of Abhyankar.- 4 Equisingularity Invariants of Plane Curves.- 5 Classification of Algebraic Space Curves, III.- 6 Plane Polynomial Curves.- III Algebraic Surfaces.- 7 A Sharp Castelnuovo Bound for the Normalization of Certain Projective Surfaces.- 8 Abhyankar's Work on Desingularization.- 9 Moduli Spaces for Special Surfaces of General Type.- IV Analytic Functions.- 10 A Stationary Phase Formula for p-ADIC Integrals and its Applications.- V Groups and Coverings.- 11 The Q-admissibility of 2A6 and 2A7.- 12 Groups Which Cannot be Realized as Fundamental Groups of the Complements to Hypersurfaces in CN.- 13 Unramified Coverings of the Affine Line in Positive Characteristic.- VI Young Tableaux.- 14 Abhyankar's Work on Young Tableaux and Some Recent Developments.- Abhyankar's Recursive Formula Regarding Standard Bi-Tableau.- 16 Correspondences Between Tableaux and Monomials.- VII Commutative Algebra.- 17 Report on the Torsion of the Differential Module of an Algebraic Curve.- 18 A Quick Proof of the Hartshorne-Lichtenbaum Vanishing Theorem.- 19 Projective Lines Over One-Dimensional Semilocal Domains and Spectra of Birational Extensions.- 20 Some Questions on Z[?14].- 21 Function Fields of Conies, a Theorem of Amitsur-MacRae, and a Problem of Zariski.- 22 Gradings of Polynomial Rings.- 23 Rigid Hilbert Polynomials for ra-Primary Ideals.- 24 One-Dimensional Local Rings with Finite Cohen-Macaulay Type.- VIII Computational Algebraic Geometry.- 25 Some Applications of Constructive Real Algebraic Geometry.- 26 An Improved Sign Determination Algorithm.- 27 DecompositionAlgorithms in Geometry.- 28 Single Exponential Path Finding in Semi-algebraic Sets, Part II: The General Case.- 29 An Improved Projection for Cylindrical Algebraic Decomposition.- 30 Degree Bounds of Gröbner Bases.- 31 Elastica and Computer Vision.- 32 Isolator Polynomials.- 33 A Bound on the Implicit Degree of Polygonal Bézier Surfaces.- IX Publications of Shreeram.
I Past, Present, and Future.- Mathematics and India.- II Algebraic Curves.- 2 Square-root Parametrization of Plane Curves.- 3 A Letter as an Appendix to the Square-Root Parameterization Paper Of Abhyankar.- 4 Equisingularity Invariants of Plane Curves.- 5 Classification of Algebraic Space Curves, III.- 6 Plane Polynomial Curves.- III Algebraic Surfaces.- 7 A Sharp Castelnuovo Bound for the Normalization of Certain Projective Surfaces.- 8 Abhyankar's Work on Desingularization.- 9 Moduli Spaces for Special Surfaces of General Type.- IV Analytic Functions.- 10 A Stationary Phase Formula for p-ADIC Integrals and its Applications.- V Groups and Coverings.- 11 The Q-admissibility of 2A6 and 2A7.- 12 Groups Which Cannot be Realized as Fundamental Groups of the Complements to Hypersurfaces in CN.- 13 Unramified Coverings of the Affine Line in Positive Characteristic.- VI Young Tableaux.- 14 Abhyankar's Work on Young Tableaux and Some Recent Developments.- Abhyankar's Recursive Formula Regarding Standard Bi-Tableau.- 16 Correspondences Between Tableaux and Monomials.- VII Commutative Algebra.- 17 Report on the Torsion of the Differential Module of an Algebraic Curve.- 18 A Quick Proof of the Hartshorne-Lichtenbaum Vanishing Theorem.- 19 Projective Lines Over One-Dimensional Semilocal Domains and Spectra of Birational Extensions.- 20 Some Questions on Z[?14].- 21 Function Fields of Conies, a Theorem of Amitsur-MacRae, and a Problem of Zariski.- 22 Gradings of Polynomial Rings.- 23 Rigid Hilbert Polynomials for ra-Primary Ideals.- 24 One-Dimensional Local Rings with Finite Cohen-Macaulay Type.- VIII Computational Algebraic Geometry.- 25 Some Applications of Constructive Real Algebraic Geometry.- 26 An Improved Sign Determination Algorithm.- 27 DecompositionAlgorithms in Geometry.- 28 Single Exponential Path Finding in Semi-algebraic Sets, Part II: The General Case.- 29 An Improved Projection for Cylindrical Algebraic Decomposition.- 30 Degree Bounds of Gröbner Bases.- 31 Elastica and Computer Vision.- 32 Isolator Polynomials.- 33 A Bound on the Implicit Degree of Polygonal Bézier Surfaces.- IX Publications of Shreeram.
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