Enumerative Real Algebraic Geometry
Abstract
Enumerative Geometry is concerned with the number of solutions to a structured system of polynomial equations, when the structure comes from geometry. Enumerative real algebraic geometry studies real solutions to such systems, particularly a priori information on their number. Recent results in this area have, often as not, uncovered new and unexpected phenomena, and it is far from clear what to expect in general. Nevertheless, some themes are emerging. This comprehensive article describe the current state of knowledge, indicating these themes, and suggests lines of future research. In particular, it compares the state of knowledge in Enumerative Real Algebraic Geometry with what is known about real solutions to systems of sparse polynomials.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 July 2001
 arXiv:
 arXiv:math/0107179
 Bibcode:
 2001math......7179S
 Keywords:

 Mathematics  Algebraic Geometry;
 14P99;
 12D10;
 14N10;
 14N15;
 14M15;
 14M25;
 14M17
 EPrint:
 Revised, corrected version. 40 pages, 18 color .eps figures. Expanded webbased version at http://www.math.umass.edu/~sottile/pages/ERAG/index.html