Enumerative Geometry for Real Varieties

  title={Enumerative Geometry for Real Varieties},
  author={Frank Sottile},
Of the geometric figures in a given family satisfying real conditions, some figures are real while the rest occur in complex conjugate pairs, and the distribution of the two types depends subtly upon the configuration of the conditions. Despite this difficulty, applications ([7],[28],[32]) may demand real solutions. Fulton [11] asked how many solutions of an enumerative problem can be real, and we consider a special case of his question: Given a problem of enumerative geometry, are there real… CONTINUE READING


Publications referenced by this paper.
Showing 1-10 of 38 references

Multivariate Descartes' rule

  • I. Itenberg, M.-F. Roy
  • Beitr age zur Algebra und Geometrie, to appear
  • 1997
Highly Influential
4 Excerpts

The number of conics tangent to 5 given conics: the real case

  • F. Ronga, A. Tognoli, T. Vust
  • manuscript, http://www.unige.ch/math/bibl…
  • 1995
Highly Influential
6 Excerpts

Eine neue Relation zwischen den Singularit aten einer algebraischen Kurve

  • F. Klein
  • Math. Ann., 10
  • 1876
Highly Influential
4 Excerpts

Construction des coniques qui satisfont a cinque conditions

  • M. Chasles
  • C. R. Acad. Sci. Paris, 58
  • 1864
Highly Influential
4 Excerpts


  • A. G. Khovanskii
  • Trans. of Math. Monographs, 88, Amer. Math. Soc.
  • 1991
Highly Influential
5 Excerpts

Newton polyhedra and the genus of complete intersections

  • A. Khovanskii
  • Funct. Anal. Appl., 12
  • 1978
Highly Influential
5 Excerpts

A Newton polyhedron and the number of solutions of a system of k equations in k unknowns

  • A. G. Kouchnirenko
  • Usp. Math. Nauk., 30
  • 1975
Highly Influential
5 Excerpts

The number of roots of a system of equations

  • D. N. Bernstein
  • Funct. Anal. Appl., 9
  • 1975
Highly Influential
5 Excerpts

Degenerations of ag and Schubert varieties into toric varieties

  • N. Goniciulea, V. Lakshmibai
  • Transfor- mation Groups, 1
  • 1996

Duality of real projective plane curves: Klein's equation

  • C. Wall
  • Topology, 35
  • 1996
3 Excerpts

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