Quintic surfaces of having a non singular model with
Ramification divisors for branched coverings of IPn.
Rank 2 vector bundles on P4 with c1 odd and contact curves.
Rational curves on hypersurfaces
Rational equivalence on some families of plane curves
If denotes the variety of irreducible plane curves of degree with exactly nodes as singularities, Diaz and Harris (1986) have conjectured that is a torsion group. In this note we study rational equivalence on some families of singular plane curves and we prove, in particular, that is a finite group, so that the conjecture holds for . Actually the order of is , the group being cyclic if is odd and the product of and a cyclic group of order if is even.
Real algebraic curves, the moment map and amoebas.
Real algebraic hypersurfaces in complex projective varieties.
Real points on complex plane curves.
Real quartic surfaces containing 16 skew lines.
Real Schubert calculus: polynomial systems and a conjecture of Shapiro and Shapiro.
Real Zeros of Positive Semidefinite Forms. I.
Recovering an algebraic curve using its projections from different points. Applications to static and dynamic computational vision
We study some geometric configurations related to projections of an irreducible algebraic curve embedded in onto embedded projective planes. These configurations are motivated by applications to static and dynamic computational vision. More precisely, we study how an irreducible closed algebraic curve embedded in , of degree and genus , can be recovered using its projections from points onto embedded projective planes. The embeddings are unknown. The only input is the defining equation of...
Refined intersection products and limiting linear subspaces of hypersurfaces.
Relative maps and tautological classes
Remarks on the Cayley-van der Waerden-Chow form.
Remarks on the postulation of zero-dimensional subschemes of projective space.
Réponse à une observation présentée dans le Giornale di Matematiche
Salvetti complex, spectral sequences and cohomology of Artin groups
The aim of this short survey is to give a quick introduction to the Salvetti complex as a tool for the study of the cohomology of Artin groups. In particular we show how a spectral sequence induced by a filtration on the complex provides a very natural and useful method to study recursively the cohomology of Artin groups, simplifying many computations. In the last section some examples of applications are presented.
Schubert and Grothendieck: a bidecennial balance. (Schubert et Grothendieck: un bilan bidécennal.)
Schur and Schubert polynomials as Thom polynomials-cohomology of moduli spaces
The theory of Schur and Schubert polynomials is revisited in this paper from the point of view of generalized Thom polynomials. When we apply a general method to compute Thom polynomials for this case we obtain a new definition for (double versions of) Schur and Schubert polynomials: they will be solutions of interpolation problems.