The multipliers of similitudes and the Brauer group of homogeneous varieties.
The Mumford conjecture
The Mumford Conjecture asserts that the rational cohomology of the stable moduli space of Riemann surfaces is a polynomial algebra on the Mumford-Morita-Miller characteristic classes; this can be reformulated in terms of the classifying space derived from the mapping class groups. The conjecture admits a topological generalization, inspired by Tillmann’s theorem that admits an infinite loop space structure after applying Quillen’s plus construction. The text presents the proof by Madsen and...
The Mumford-Tate group of 1-motives
In this paper we study the structure and the degeneracies of the Mumford-Tate group of a 1-motive defined over . This group is an algebraic - group acting on the Hodge realization of and endowed with an increasing filtration . We prove that the unipotent radical of , which is , injects into a “generalized” Heisenberg group. We then explain how to reduce to the study of the Mumford-Tate group of a direct sum of 1-motives whose torus’character group and whose lattice are both of rank 1....
The Nash conjecture for threefolds.
The Nash problem of arcs and the rational double points
This paper deals with the Nash problem, which consists in comparing the number of families of arcs on a singular germ of surface with the number of essential components of the exceptional divisor in the minimal resolution of this singularity. We prove their equality in the case of the rational double points ().
The Néron Fiber of Abelian Varieties with Potential Good Reduction.
The Neron model for families of intermediate jacobians acquiring “algebraic” singularities
The Néron-Severi group and the mixed Hodge structure on H2.
The Neuberg cubic in locus problems.
The nil Hecke ring and singularity of Schubert varieties.
The Noether-Lefschetz theorem and sums of 4 squares in the rational function field
The non rationality of the generic Enriques' threefold
The non-existence of a smooth sectionally non-special surface of degree 11 and sectional genus 8 in the projective fourspace.
The nonreduced order spectrum of a commutative ring.
The Normal Bundle of a Curve on a Quadric.
The normality of closures of conjugacy classes of matrices.
The normality of closures of orbits in a Lie algebra.
The Normalizer of the level (2,2)-Heisenberg Group.
The Nullstellensatz for real coherent analytic surfaces.
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.