论文信息 - Viro Method for the Construction of Real Complete Intersections

Viro Method for the Construction of Real Complete Intersections

Abstract The Viro method is a powerful construction method of real nonsingular algebraic hypersurfaces with prescribed topology. It is based on polyhedral subdivisions of Newton polytopes. A combinatorial version of the Viro method is called combinatorial patchworking and arises when the considered subdivisions are triangulations. B. Sturmfels has generalized the combinatorial patchworking to the case of real complete intersections. We extend his result by generalizing the Viro method to the case of real complete intersections.

Frédéric Bihan | Frédéric Bihan

[1] Marie-Hélène Schwartz. Champs radiaux sur une stratification analytique , 1991 .

[2] A. Vershik,et al. Topology, Ergodic Theory, Real Algebraic Geometry: Rokhlin’s Memorial , 2001 .

[3] E. Shustin,et al. Singular points and limit cycles of planar polynomial vector fields , 2000 .

[4] Bernd Sturmfels,et al. On the Newton Polytope of the Resultant , 1994 .

[5] Ilia Itenberg,et al. Topology of real algebraic T-surfaces. , 1997 .

[6] Birkett Huber,et al. The Cayley Trick, lifting subdivisions and the Bohne-Dress theorem on zonotopal tilings , 2000 .

[7] Bernd Sturmfels. Viro's theorem for complete intersections , 1994 .

[8] I. M. Gelʹfand,et al. Discriminants, Resultants, and Multidimensional Determinants , 1994 .

[9] B. Chevallier. Secteurs et déformations locales de courbes réelles , 1997 .

[10] E. Shustin. Real plane algebraic curves with prescribed singularities , 1993 .