Polynomial Cycles in Finitely Generated Domains.
Polynomial inequalities on algebraic sets
We give an estimate of Siciak’s extremal function for compact subsets of algebraic varieties in (resp. ). As an application we obtain Bernstein-Walsh and tangential Markov type inequalities for (the traces of) polynomials on algebraic sets.
Polynomial invariants of representations of quivers.
Polynomial mappings form products of algebraic sets into spheres.
Polynomial periodicity for Betti numbers of covering surfaces.
Polynomial Ring in Two Variables Over a D.V.R.: A Criterion.
Polynomial structures and generic Torelli for projective hypersurfaces
Polynomials homologically supported on degeneracy loci
Polynomials, Symmetry, and Dynamics: an Undertaking in Aesthetics
Polynomials with high multiplicity
Polynomials with integral coefficients, equivalent to a given polynomial.
Polynomial-time computation of the degree of a dominant morphism in zero characteristic. II.
Polytopal linear algebra.
Polytopes, quasi-minuscule representations and rational surfaces
We describe the relation between quasi-minuscule representations, polytopes and Weyl group orbits in Picard lattices of rational surfaces. As an application, to each quasi-minuscule representation we attach a class of rational surfaces, and realize such a representation as an associated vector bundle of a principal bundle over these surfaces. Moreover, any quasi-minuscule representation can be defined by rational curves, or their disjoint unions in a rational surface, satisfying certain natural...
Polytopes secondaires et discriminants
Poncelet 5-gons and abelian surfaces.
Positive Curves in Polarized Manifolds.
Positive polynomials and hyperdeterminants
Let F be a homogeneous real polynomial of even degree in any number of variables. We consider the problem of giving explicit conditions on the coefficients so that F is positive definite or positive semi-definite. In this note we produce a necessary condition for positivity, and a sufficient condition for non-negativity, in terms of positivity or semi-positivity of a one-variable characteristic polynomial of F. Also, we revisit the known sufficient condition in terms of Hankel matrices.
Positive sheaves of differentials coming from coarse moduli spaces
Consider a smooth projective family of canonically polarized complex manifolds over a smooth quasi-projective complex base , and suppose the family is non-isotrivial. If is a smooth compactification of , such that is a simple normal crossing divisor, then we can consider the sheaf of differentials with logarithmic poles along . Viehweg and Zuo have shown that for some , the symmetric power of this sheaf admits many sections. More precisely, the symmetric power contains an invertible...
Positive Vector Bundles on Complex Surfaces.