**Contemporary Mathematics**

Volume: 496;
2009;
362 pp;
Softcover

MSC: Primary 13; 14; 65;

Print ISBN: 978-0-8218-4746-6

Product Code: CONM/496

List Price: $105.00

AMS Member Price: $84.00

MAA Member Price: $94.50

**Electronic ISBN: 978-0-8218-8175-0
Product Code: CONM/496.E**

List Price: $105.00

AMS Member Price: $84.00

MAA Member Price: $94.50

# Interactions of Classical and Numerical Algebraic Geometry

Share this page *Edited by *
*Daniel J. Bates; GianMario Besana; Sandra Di Rocco; Charles W. Wampler*

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.

#### Readership

Graduate students and research mathematicians interested in algebraic geometry, numerical methods, and applications in engineering.

# Table of Contents

## Interactions of Classical and Numerical Algebraic Geometry

- Contents vii8 free
- Preface ix10 free
- Turning points and bifurcations for homotopies of analytic maps 116 free
- On a connectedness theorem of Debarre 1126
- Stepsize control for path tracking 2136
- A primer on Seshadri constants 3348
- 1. Definitions 3449
- 2. Basic properties 3651
- 3. Projective spaces 4055
- 4. Toric varieties 4257
- 5. Slope stability and Seshadri constants 4459
- 6. Seshadri constants on surfaces 4762
- 7. S-slope and fibrations by Seshadri curves 5671
- 8. Algebraic manifestation of Seshadri constants 5974
- References 6782

- A view on extending morphisms from ample divisors 7186
- 1. Introduction 7186
- 2. Background material 7388
- 3. General results 7893
- 4. Some convex geometry speculations 85100
- 5. Applications to Pd-bundles and blowing-ups 89104
- 6. Complete results in the three dimensional case 95110
- 7. Extending P1-bundles 97112
- 8. Fano manifolds as ample divisors 102117
- 9. Ascent properties 104119
- Acknowledgments 107122
- References 108123

- Isotropic models of evolution with symmetries 111126
- Special scrolls whose base curve has general moduli 133148
- On varieties whose universal cover is a product of curves (with an appendix by A. J. Di Scala) 157172
- Ideals of numeric realizations of configurations of lines 181196
- The standard filtration on cohomology with compact supports with an appendix on the base change map and the Lefschetz hyperplane theorem 199214
- A family of exceptional Stewart Gough mechanisms of genus 7 221236
- Numerical computation of the dimensions of the cohomology of twists of ideal sheaves 235250
- Polyhedral methods in numerical algebraic geometry 243258
- Double covers of Del Pezzo manifolds and bielliptic curve sections 265280
- Total degree vs. mixed volume 283298
- Varieties swept out by Grassmanians of lines 303318
- Submanifolds with ample normal bundles and a conjecture of Hartshorne 317332
- A complete kinematic analysis of the SNU 3-UPU parallel robot 331346
- The closedness subspace method for computing the multiplicity structure of a polynomial system 347362