Algebraic Geometry and Its Applications : Collections of Papers From Shreeram S. Abhyankar’s 60th Birthday Conference

**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. Front Matter....Pages i-xxii Front Matter....Pages 1-1 Mathematics and India....Pages 3-15 Front Matter....Pages 17-17 Square-root Parametrization of Plane Curves....Pages 19-84 A Letter as an Appendix to the Square-Root Parameterization Paper Of Abhyankar....Pages 85-88 Equisingularity Invariants of Plane Curves....Pages 89-112 Classification of Algebraic Space Curves, III....Pages 113-120 Plane Polynomial Curves....Pages 121-142 Front Matter....Pages 143-143 A Sharp Castelnuovo Bound for the Normalization of Certain Projective Surfaces....Pages 145-151 Abhyankar’s Work on Desingularization....Pages 153-160 Moduli Spaces for Special Surfaces of General Type....Pages 161-172 Front Matter....Pages 173-173 A Stationary Phase Formula for p -ADIC Integrals and its Applications....Pages 175-194 Front Matter....Pages 195-195 The Q-admissibility of 2 A 6 and 2 A 7 ....Pages 197-202 Groups Which Cannot be Realized as Fundamental Groups of the Complements to Hypersurface in C N ....Pages 203-207 Unramified Coverings of the Affine Line in Positive Characteristic....Pages 209-212 Front Matter....Pages 213-213 Abhyankar’s Work on Young Tableaux and Some Recent Developments....Pages 215-249 Abhyankar’s Recursive Formula Regarding Standard Bi-Tableau....Pages 251-259 Correspondences Between Tableaux and Monomials....Pages 261-281 Front Matter....Pages 283-283 Report on the Torsion of Differential Module of an Algebraic Curve....Pages 285-303 A Quick Proof of the Hartshorne-Lichtenbaum Vanishing Theorem....Pages 305-308 Projective Lines Over One-Dimensional Semilocal Domains and Spectra of Birational Extensions....Pages 309-325 Some Questions on Z[√14]....Pages 327-332 Front Matter....Pages 283-283 Function Fields of Conies, a Theorem of Amitsur—MacRae, and a Problem of Zariski....Pages 333-363 Gradings of Polynomial Rings....Pages 365-373 Rigid Hilbert Polynomials for m -Primary Ideals....Pages 375-379 One-Dimensional Local Rings with Finite Cohen-Macaulay Type....Pages 381-389 Front Matter....Pages 391-391 Some Applications of Constructive Real Algebraic Geometry....Pages 393-405 An Improved Sign Determination Algorithm....Pages 407-418 Decomposition Algorithms in Geometry....Pages 419-447 Single Exponential Path Finding in Semi-algebraic Sets, Part II: The General Case....Pages 449-465 An Improved Projection for Cylindrical Algebraic Decomposition....Pages 467-476 Degree Bounds of Gröbner Bases....Pages 477-490 Elastica and Computer Vision....Pages 491-506 Isolator Polynomials....Pages 507-512 A Bound on the Implicit Degree of Polygonal Bézier Surfaces....Pages 513-525