Related papers: D\'eformations des courbes rationnelles

We give a counterexample to the proof in the literature [K-Theory 25 (2002), 215-231] of the existence of linear representatives of higher Chow groups of number fields.

We develop direct and inverse scattering theory for Jacobi operators (doubly infinite second order difference operators) with steplike coefficients which are asymptotically close to different finite-gap quasi-periodic coefficients on…

We study the Toda conjecture of Eguchi and Yang for the Gromov-Witten invariants of CP^1,using the bihamiltonian method of the formal calculus of variations. We also study its relationship to the Virasoro conjecture for CP^1, recently…

In this lecture we prove a converse to Cartan's Theorem B for real analytic sets, due to Fernando and Ghiloni [arXiv:2506.18347].

We give a negative answer to a question by J.M. Landsberg on the nature of normalizations of orbit closures. A counterexample originates from the study of complex, ternary, cubic forms.

This paper has been withdrawn by the author.

A dynamical Mertens' theorem for ergodic toral automorphisms with error term O(N^{-1}) is found, and the influence of resonances among the eigenvalues of unit modulus is examined. Examples are found with many more, and with many fewer,…

We give a dynamical, relatively elementary proof of an "absorption theorem" which is closely related to a well-known result due to Matui. The construction is in the spirit of an earlier joint work of the author and S. Robert. In an appendix…

Regular variation of distributional tails is known to be preserved by various linear transformations of some random structures. An inverse problem for regular variation aims at understanding whether the regular variation of a transformed…

This article contains counterexamples to theorems and claims in Brams, Jones and Klamler's article "Better Ways to Cut a Cake" in the December 2006 Notices of the American Mathematical Society.

A stability version of the reverse isoperimetric inequality, and the corresponding inequality for isotropic measures are established.

We report new hypergeometric constructions of rational approximations to Catalan's constant, $\log2$, and $\pi^2$, their connection with already known ones, and underlying "permutation group" structures. Our principal arithmetic achievement…

A vector variational principle is proved.

In this note a two sided bound on the tail probability of sums of independent, and either symmetric or nonnegative, random variables is obtained. We utilize a recent result by Lata{\l}a on bounds on moments of such sums. We also give a new…

Twisted vertex operators based on rational lattices have had many applications in vertex operator algebra theory and conformal field theory. In this paper, ``relativized'' twisted vertex operators are constructed in a general context based…

Two transforms of functions on a half-line are considered. It is proved that their composition gives a concave majorant for every nonnegative function. In particular, this composition is the identity transform on the class of nonnegative…

We establish a real version of Turrittin's result on polynomial and formal normal forms of linear systems of ODEs with meromorphic coefficients. Both the normal forms or the transformations used have only real coefficients. In order to…

An equivalent but useful version on the Homological Nerve Theorem is proved.

Preliminary results from Nathanson [5] are used to prove the Muirhead and Rado inequalities.

We prove a version of Rao decomposition for quasi-martingales indexed by a linearly ordered set.