enumerative geometry

**Enumerative geometry** is a branch of algebraic geometry which counts a number of solutions to various geometric problems, usually stated for data in *general position*. Usually the solution is a nonnegative integer, but some vaguely defined intuitive enumerative problems have rigorous reformulations in terms of integration on moduli spaces and can yield answers which are, say, rational numbers. Most studied enumerative problems are problems of intersection theory of algebraic subvarieties and the solution is often found by cohomological methods.

How many plane conics are tangent simultaneously to 5 given plane conics in general position ? The answer is 3264, see Griffiths-Harris, *Principles of algebraic geometry* for a detailed treatment. A further question is how many of them are real ? see Frank Sottile, 3264 real curves.

- intersection theory
- Gromov-Witten invariant
- Schubert calculus
- wikipedia enumerative geometry
- William Fulton,
*Introduction to intersection theory in algebraic geometry*, CBMS 54, AMS, 1996, second edition

Created on November 2, 2012 at 19:30:40. See the history of this page for a list of all contributions to it.