## Interactions of Classical and Numerical Algebraic Geometry: A Conference in Honor of Andrew Sommese : Interactions of Classical and Numerical Algebraic Geometry, May 22-24, 2008, University of Notre Dame, Notre Dame, IndianaThis 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. |

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

1 | |

On a connectedness theorem of Debarre | 11 |

Stepsize control for path tracking | 21 |

A primer on Seshadri constants | 33 |

A view on extending morphisms from ample divisors | 71 |

Isotropic models of evolution with symmetries | 111 |

Special scrolls whose base curve has general moduli | 133 |

On varieties whose universal cover is a product of curves with an appendix | 161 |

Numerical computation of the dimensions of the cohomology of twists of ideal | 235 |

Polyhedral methods in numerical algebraic geometry | 243 |

Double covers of Del Pezzo manifolds and bielliptic curve sections | 265 |

vii | 278 |

Total degree vs mixed volume | 283 |

Varieties swept out by Grassmanians of lines | 303 |

Submanifolds with ample normal bundles and a conjecture of Hartshorne | 317 |

A complete kinematic analysis of the SNU 3UPU parallel robot | 331 |

Ideals of numeric realizations of configurations of lines | 181 |

The standard filtration on cohomology with compact supports with | 199 |

A family of exceptional Stewart Gough mechanisms of genus 7 | 221 |

The closedness subspace method for computing the multiplicity structure of | 347 |

### Other editions - View all

Interactions of Classical and Numerical Algebraic Geometry Andrew John Sommese No preview available - 2009 |

### Common terms and phrases

abelian algebraic curves algebraic geometry algorithm ample divisor ample line bundle assume base change maps canonical codimension cohomology groups complex compute consider construction contained Corollary corresponding deﬁned degree Del Pezzo surface denote double covering double-six elliptic embedding equations exact sequence example exists extremal ray Fano manifold ﬁber finite ﬁrst genus g given hence Hilbert function Hilbert polynomial Hilbert scheme homotopy hyperplane sections hypersurface integer intersection irreducible components isomorphism K3 surface Lefschetz Lemma Leray filtration Let f linear system linearly normal manifold of dimension Math Mathematics matrix mixed volume model of evolution moduli monomial morphism multiplicity normal bundle notation Note parameters Pezzo manifolds polyhedral polynomial system projective manifold projective space projective variety proof Proposition Puiseux series quadric rational curves Remark result Seshadri constants singular solution special tensor subgroup subspace subvariety surjective symmetric Theorem tropisms universal cover vector bundle zero