Solutions de quelques problèmes relatifs aux surfaces du second degré.
Solutions d'équations à coefficients dans un anneau hensélien
Solutions to the XXX type Bethe ansatz equations and flag varieties
We consider a version of the A N Bethe equation of XXX type and introduce a reporduction procedure constructing new solutions of this equation from a given one. The set of all solutions obtained from a given one is called a population. We show that a population is isomorphic to the sl N+1 flag variety and that the populations are in one-to-one correspondence with intersection points of suitable Schubert cycles in a Grassmanian variety. We also obtain similar results for the root systems B N and...
Solving algebraic equations in roots of unity.
Solving an indeterminate third degree equation in rational numbers. Sylvester and Lucas
This article concerns the problem of solving diophantine equations in rational numbers. It traces the way in which the 19th century broke from the centuries-old tradition of the purely algebraic treatment of this problem. Special attention is paid to Sylvester’s work “On Certain Ternary Cubic-Form Equations” (1879–1880), in which the algebraico-geometrical approach was applied to the study of an indeterminate equation of third degree.
Solving the equation x3 - y2 = r in number fields.
Solving the quintic by iteration in three dimensions.
Solving the sextic by iteration: a study in complex geometry and dynamics.
Some abelian threefolds with nontrivial Griffiths group
Some Algebraicity Criteria for Singular Surfaces.
Some analogies between number theory and dynamical systems on foliated spaces.
Some analogs of Zariski's Theorem on nodal line arrangements.
Some Applications of the Resultant
Some applications of the theory of harmonic integrals
In this survey, we present recent techniques on the theory of harmonic integrals to study the cohomology groups of the adjoint bundle with the multiplier ideal sheaf of singular metrics. As an application, we give an analytic version of the injectivity theorem.
Some applications of the trace mapping for differentials
Some approximation problems in semi-algebraic geometry
In this paper we deal with a best approximation of a vector with respect to a closed semi-algebraic set C in the space ℝⁿ endowed with a semi-algebraic norm ν. Under additional assumptions on ν we prove semi-algebraicity of the set of points of unique approximation and other sets associated with the distance to C. For C irreducible algebraic we study the critical point correspondence and introduce the ν-distance degree, generalizing the notion developed by other authors for the Euclidean norm. We...
Some basic facts in algebraic geometry on a non algebraically closed field
Some birational maps of Fano 3-folds
Some boundedness results for Fano-like Moishezon manifolds.
Some characteristic numbers for nodal and cuspidal plane curves of any degree.