F. Sottile, "Real enumerative geometry and effective algebraic equivalence", J. Pure Appl. Algebra 117/118 (1997), 601--615. Home/Search Document Details and Download
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Algebraic Geometry and Computer Vision: Polynomial Systems, Real .. - Petitjean (1998) (1 citation) (Correct)
....of some real Euclidean space that are defined by polynomial equalities and inequalities) and algorithms on these sets. This means that the name does not usually cover some of the techniques of algebraic geometry working over the reals (like real intersection theory and enumerative geometry [28, 97]) In the sequel, we focus on some of the most efficient and recent techniques for dealing with algebraic equation systems, over the reals and over the complexes. Section 2 starts by recalling which geometric reasoning problems stirred to do research on efficiently solving polynomial systems. ....
....can be real. For instance, 83] investigated the number of conics tangent to five general conics in the real case. They proved that in fact all (i.e. 3264 as was found by de Jonqui eres in 1859, and again by Chasles in 1864 see [116] can be real. In a recent series of papers, F. Sottile [95, 96, 97] was the first to give a general statement in this direction: he produces large classes of fully real non trivial enumerative problems. For instance, he proves in [96] that for any problem of enumerating lines in P n incident on real linear subspaces in general position, all solutions can be ....
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F. Sottile. Real enumerative geometry and effective algebraic equivalence. In Proceedings of 4th Mega (International Symposium on Effective Methods in Algebraic Geometry), Eindhoven, The Netherlands, 1996. 32 Petitjean
Real Schubert Calculus: Polynomial Systems and a Conjecture of.. - Sottile (1998) (8 citations) Self-citation (Sottile) (Correct)
....Counterexample 5.1 involves Grassmannian Schubert data. Let F (2; n Gamma2; n) be the manifold of flags X ae Y in C n where dimX = 2 and dimY = n Gamma 2. 4 June 2000 at 14:57 Sottile: Real Schubert Calculus: Polynomial Systems and a Conjecture of Shapiro and Shapiro 179 Proposition 5. 2 [Sottile 1997c, Theorem 13] Given any Grassmannian Schubert data for F (2; n Gamma2; n) there exist real flags whose corresponding Schubert varieties meet transversally with all points of intersection real . The beauty of the conjectures of Shapiro and Shapiro is that they give a simple algorithm for ....
F. Sottile, "Real enumerative geometry and effective algebraic equivalence", J. Pure Appl. Algebra 117/118 (1997), 601--615.
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