From Symplectic Packing to Algebraic Geometry and Back
In this paper we survey various aspects of the symplectic packing problem and its relations to algebraic geometry, going through results of Gromov, McDuff, Polterovich and the author.
Topics in Combinatorial Algebraic Geometry
This thesis consists of six papers in algebraic geometry –all of which have close connections to combinatorics. In Paper A we consider complete smooth toric embeddings X ↪ P^N such that for a fixed…
Invent. Math., 66(3):481–491, 1982.
son. Algebraic K-theory eventually surjects onto topological K-theory.
Commutative Algebra: with a View Toward Algebraic Geometry
Introduction.- Elementary Definitions.- I Basic Constructions.- II Dimension Theory.- III Homological Methods.- Appendices.- Hints and Solutions for Selected Exercises.- References.- Index of…
Projective geometry and homological algebra
We provide an introduction to many of the homological commands in Macaulay 2 (modules, free resolutions, Ext and Tor. ..) by means of examples showing how to use homological tools to study projective…
Introduction to numerical algebraic geometry
In a 1996 paper, Andrew Sommese and Charles Wampler began developing a new area, “Numerical Algebraic Geometry”, which would bear the same relation to “Algebraic Geometry” that “Numerical Linear…
A Characterization of Affine Varieties
Here we give a cohomological condition for the affiness of an algebraic scheme. Mathematics Subject Classification: 14F17; 32E10
Lie groups, Nahm's equations and hyperkaehler manifolds
Lectures given at the summer school on Algebraic Groups, Goettingen, June 27 - July 15 2005
Topics in computation, numerical methods and algebraic geometry
This thesis concerns computation and algebraic geometry. On the computational side we have focused on numerical homotopy methods. These procedures may be used to numerically solve systems of polyno…