Enumerative Real Algebraic Geometry

Details Enumerative Real Algebraic Geometry Enumerative Real Algebraic Geometry

2001-07-24

arxiv.org/abs/math/0107179v2

in Algorithmic and Quantitative Aspects of Real Algbraic Geometry, S. Basu and L. Gonzalez-Vega, eds., DIMACS series 60, AMS,

Mathematics

Algebraic Geometry

Revised, corrected version. 40 pages, 18 color .eps figures. Expanded web-based version at http://www.math.umass.edu/~sottile/

Scientific paper

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.

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