On global Nash functions
On glueing curves on surfaces and zero cycles
The structure of the group of a surface with prescribed singularities is investigated.
On graded Bett numbers and geometrical properties of projective varieties.
On gradient at infinity of semialgebraic functions
Let f: ℝⁿ → ℝ be a C² semialgebraic function and let c be an asymptotic critical value of f. We prove that there exists a smallest rational number such that |x|·|∇f| and are separated at infinity. If c is a regular value and , then f is a locally trivial fibration over c, and the trivialisation is realised by the flow of the gradient field of f.
On gradients of functions definable in o-minimal structures
We prove the o-minimal generalization of the Łojasiewicz inequality , with , in a neighborhood of , where is real analytic at and . We deduce, as in the analytic case, that trajectories of the gradient of a function definable in an o-minimal structure are of uniformly bounded length. We obtain also that the gradient flow gives a retraction onto levels of such functions.
On Grothendieck's generalized Hodge conjecture for a family of threefolds with trivial canonical bundle.
On Grothendieck's pairing of component groups in the semistable reduction case.
On Harder-Narashimhan stratification over Quot schemes.
On Hecke Polynomials.
On Heron triangles.
On higher dimensional Hirzebruch-Jung singularities.
A germ of normal complex analytical surface is called a Hirzebruch-Jung singularity if it is analytically isomorphic to the germ at the 0-dimensional orbit of an affine toric surface. Two such germs are known to be isomorphic if and only if the toric surfaces corresponding to them are equivariantly isomorphic. We extend this result to higher-dimensional Hirzebruch-Jung singularities, which we define to be the germs analytically isomorphic to the germ at the 0-dimensional orbit of an affine toric...
On higher-order weierstrass points and the finiteness of the automorphism group.
On Hilbert polynomial of certain determinantal ideals.
On Hilbert's 17th Problem and Real Nullstellensatz for Global Analytic Functions.
On Hironaka's Additive Groups Associated with Points in Projective Space.
On Hodge structures and non-representability of Chow groups
On Holomorphic Curves in Algebraic Varieties with Ample Regularity.
On homology classes represented by real algebraic varieties
On homology of real algebraic sets.
On homotopy types of limits of semi-algebraic sets and additive complexity of polynomials
We prove that the number of distinct homotopy types of limits of one-parameter semi-algebraic families of closed and bounded semi-algebraic sets is bounded singly exponentially in the additive complexity of any quantifier-free first order formula defining the family. As an important consequence, we derive that the number of distinct homotopy types of semi-algebraic subsets of defined by a quantifier-free first order formula , where the sum of the additive complexities of the polynomials appearing...