Macaulay's theorem and local Torelli for weighted hypersurfaces
Mahler's measure: proof of two conjectured formulae.
Majorations affines du nombre de zéros d'intégrales abéliennes pour les hamiltoniens quartiques elliptiques
Manifolds with a unique embedding
We show that if X, Y are smooth, compact k-dimensional submanifolds of ℝⁿ and 2k+2 ≤ n, then each diffeomorphism ϕ: X → Y can be extended to a diffeomorphism Φ: ℝⁿ → ℝⁿ which is tame (to be defined in this paper). Moreover, if X, Y are real analytic manifolds and the mapping ϕ is analytic, then we can choose Φ to be also analytic. We extend this result to some interesting categories of closed (not necessarily compact) subsets of ℝⁿ, namely, to the category of Nash submanifolds...
Manin’s and Peyre’s conjectures on rational points and adelic mixing
Let be the wonderful compactification of a connected adjoint semisimple group defined over a number field . We prove Manin’s conjecture on the asymptotic (as ) of the number of -rational points of of height less than , and give an explicit construction of a measure on , generalizing Peyre’s measure, which describes the asymptotic distribution of the rational points on . Our approach is based on the mixing property of which we obtain with a rate of convergence.
Manin’s conjecture for a quartic del Pezzo surface with singularity
The Manin conjecture is established for a split singular del Pezzo surface of degree four, with singularity type .
Manin’s conjecture for a singular sextic del Pezzo surface
We prove Manin’s conjecture for a del Pezzo surface of degree six which has one singularity of type . Moreover, we achieve a meromorphic continuation and explicit expression of the associated height zeta function.
Manin's conjecture for two quartic del Pezzo surfaces with 3A₁ and A₁ + A₂ singularity types
Manin's conjecture on a nonsingular quartic del Pezzo surface
Manis valuations and Prüfer extensions
Manis valuations and Prüfer extensions. I.
Mapping threefolds onto three-dimensional quadrics.
Mappings of the sets of invariant subspaces of null systems.
Maps defined by Thetanullwerte.
Maps of toric varieties in Cox coordinates
The Cox ring provides a coordinate system on a toric variety analogous to the homogeneous coordinate ring of projective space. Rational maps between projective spaces are described using polynomials in the coordinate ring, and we generalise this to toric varieties, providing a unified description of arbitrary rational maps between toric varieties in terms of their Cox coordinates. Introducing formal roots of polynomials is necessary even in the simplest examples.
Maps onto certain Fano threefolds.
Matching local Witt invariants
The starting point of this note is the observation that the local condition used in the notion of a Hilbert-symbol equivalence and a quaternion-symbol equivalence — once it is expressed in terms of the Witt invariant — admits a natural generalisation. In this paper we show that for global function fields as well as the formally real function fields over a real closed field all the resulting equivalences coincide.
Mathematical instanton bundles on P2n+1.
Mather discrepancy and the arc spaces
A goal of this paper is a characterization of singularities according to a new invariant, Mather discrepancy. We also show some evidences convincing us that Mather discrepancy is a reasonable invariant in a view point of birational geometry.
Matrice magique associée à un germe de courbe plane et division par l’idéal jacobien
Nous nous donnons, dans l’anneau des germes de fonctions holomorphes à l’origine de , une fonction définissant une singularité isolée et nous nous intéressons à l’équation , lorsque la fonction est donnée. Nous introduisons les multiplicités d’intersection relatives de et le long des branches de et nous étudions les solutions à l’aide de ces valuations. Grâce aux résultats ainsi démontrés, nous construisons explicitement une équation fonctionnelle vérifiée par .