Interactions of Classical and Numerical Algebraic Geometry
About this Title
Daniel J. Bates, GianMario Besana, Sandra Di Rocco and Charles W. Wampler, Editors
This volume contains the proceedings of the conference on Interactions of Classical and Numerical Algebraic Geometry, held May 22–24, 2008, at the University of Notre Dame, in honor of the achievements of Professor Andrew J. Sommese.
While classical algebraic geometry has been studied for hundreds of years, numerical algebraic geometry has only recently been developed. Due in large part to the work of Andrew Sommese and his collaborators, the intersection of these two fields is now ripe for rapid advancement. The primary goal of both the conference and this volume is to foster the interaction between researchers interested in classical algebraic geometry and those interested in numerical methods.
The topics in this book include (but are not limited to) various new results in complex algebraic geometry, a primer on Seshadri constants, analyses and presentations of existing and novel numerical homotopy methods for solving polynomial systems, a numerical method for computing the dimensions of the cohomology of twists of ideal sheaves, and the application of algebraic methods in kinematics and phylogenetics.
Graduate students and research mathematicians interested in algebraic geometry, numerical methods, and applications in engineering.
Table of Contents
- Eugene Allgower, Stefan-Gicu Cruceanu and Simon J. Tavener – Turning points and bifurcations for homotopies of analytic maps [MR 2555946]
- Lucian Bădescu – On a connectedness theorem of Debarre [MR 2555947]
- Daniel J. Bates, Jonathan D. Hauenstein, Andrew J. Sommese and Charles W. Wampler, II – Stepsize control for path tracking [MR 2555948]
- Thomas Bauer, Sandra Di Rocco, Brian Harbourne, Michał Kapustka, Andreas Knutsen, Wioletta Syzdek and Tomasz Szemberg – A primer on Seshadri constants [MR 2555949]
- Mauro C. Beltrametti and Paltin Ionescu – A view on extending morphisms from ample divisors [MR 2555950]
- Weronika Buczyńska, Maria Donten and Jarosław A. Wiśniewski – Isotropic models of evolution with symmetries [MR 2555951]
- A. Calabri, C. Ciliberto, F. Flamini and R. Miranda – Special scrolls whose base curve has general moduli [MR 2555952]
- Fabrizio Catanese and Marco Franciosi – On varieties whose universal cover is a product of curves [MR 2555953]
- Barry H. Dayton – Ideals of numeric realizations of configurations of lines [MR 2555954]
- Mark Andrea A. de Cataldo – The standard filtration on cohomology with compact supports with an appendix on the base change map and the Lefschetz hyperplane theorem [MR 2555955]
- Florian Geiß and Frank-Olaf Schreyer – A family of exceptional Stewart-Gough mechanisms of genus 7 [MR 2555956]
- Jonathan D. Hauenstein, Juan C. Migliore, Chris Peterson and Andrew J. Sommese – Numerical computation of the dimensions of the cohomology of twists of ideal sheaves [MR 2555957]
- Jan Verschelde – Polyhedral methods in numerical algebraic geometry [MR 2555958]
- Antonio Lanteri and Hidetoshi Maeda – Double covers of del Pezzo manifolds and bielliptic curve sections [MR 2555959]
- T. Y. Li, X. Wang and Y. Zhang – Total degree vs. mixed volume [MR 2555960]
- Roberto Muñoz and Luis E. Solá Conde – Varieties swept out by Grassmannians of lines [MR 2555961]
- Thomas Peternell – Submanifolds with ample normal bundles and a conjecture of Hartshorne [MR 2555962]
- Dominic R. Walter, Manfred L. Husty and Martin Pfurner – A complete kinematic analysis of the SNU 3-UPU parallel robot [MR 2555963]
- Zhonggang Zeng – The closedness subspace method for computing the multiplicity structure of a polynomial system [MR 2555964]