The hyperosculating points of surfaces in
The intersection conics of six straight lines.
The Maximal Number of Quotient Singularities on Surfaces with Given Numerical Invariants.
The Missing Seventh Circle.
The number of conics tangent to five given conics: the real case.
It is a classical result, first established by de Jonquières (1859), that generically the number of conics tangent to 5 given conics in the complex projective plane is 3264. We show here the existence of configurations of 5 real conics such that the number of real conics tangent to them is 3264.
The number of points on certain families of hypersurfaces over finite fields
The Number of Rational Quartics on Calabi-Yau Hypersurfaces in Weighted Projective Space P (2,1...).
The number of reducible hypersurfaces in a pencil.
The number of reducible hypersurfaces in a pencil (Erratum).
The Number of Twisted Cubic Curves on the General Quintic Threefold.
The Placement of Electronic Circuits Problem: A Neural Network Approach
The goal of this paper is to apply the Continuous Hopfield Networks (CHN) to the Placement of Electronic Circuit Problem (PECP). This assignment problem has been expressed as Quadratic Knapsack Problem (QKP). To solve the PECP via the CHN, we choose an energy function which ensures an appropriate balance between minimization of the cost function and simultaneous satisfaction of the PECP constraints. In addition, the parameters of this function must...
The special Schubert calculus is real.
The transversality of a general translate
The Uniform Position Principle for Curves in Characteristic p.
Thom polynomials and Schur functions: the singularities
We give the Thom polynomials for the singularities associated with maps with parameter . Our computations combine the characterization of Thom polynomials via the “method of restriction equations” of Rimanyi et al. with the techniques of Schur functions.
Thom polynomials and Schur functions: the singularities
We give a closed formula for the Thom polynomials of the singularities in terms of Schur functions. Our computations combine the characterization of the Thom polynomials via the “method of restriction equations” of Rimányi et al. with the techniques of Schur functions.
Topologische Typen reeller kubischer Flächen.
Topology of arrangements and position of singularities
This work contains an extended version of a course given in Arrangements in Pyrénées. School on hyperplane arrangements and related topics held at Pau (France) in June 2012. In the first part, we recall the computation of the fundamental group of the complement of a line arrangement. In the second part, we deal with characteristic varieties of line arrangements focusing on two aspects: the relationship with the position of the singular points (relative to projective curves of some prescribed degrees)...
Torsion in elliptic curves over
Über die Moduln algebraischer Flächen.