Related papers: Gromov Ellipticity and subellipticity
We survey on algebraically elliptic varieties in the sense of Gromov.
We construct examples of nodal quartic double solids that admit uniformly rational, and so elliptic in Gromov' sense, small algebraic resolutions.
We prove that every nontrivial principal $G_m$-bundle over a complete uniformly rational variety is algebraically elliptic in the sense of Gromov.
We show that the algebraic and the symplectic GW-inivariants of smooth projective varieties are equivalent.
For a complex projective manifold Gromov-Witten invariants can be constructed either algebraically or symplectically. Using the versions of Gromov-Witten theory by Behrend and Fantechi on the algebraic side and by the author on the…
We show that every smooth cubic hypersurface X in P^{n+1}, n> 1 is algebraically elliptic in Gromov's sense. This gives the first examples of non-rational projective manifolds elliptic in Gromov's sense. We also deduce that the punctured…
We prove that Gromov's ellipticity condition $\mathrm{Ell}_1$ characterizes Oka manifolds. This characterization gives another proof of the fact that subellipticity implies the Oka property, and affirmative answers to Gromov's conjectures.…
After reformulating Gromov's non-squeezing theorem as an area-inequality, we discuss a seemingly natural higher dimensional generalization.
We find classes of projective manifolds that are elliptic in the sense of Gromov and such that the affine cones over these manifolds also are elliptic off their vertices. For example, the latter holds for any generalized flag manifold of…
We prove, in the context of Hilbert geometry, the equivalence between the existence of an upper bound on the area of ideal triangles and the Gromov-hyperbolicity.
We formulate and study an extension of gerbe duality to relative Gromov-Witten theory.
In this paper, we introduce the concept of quasihyperbolically visible spaces. As a tool, we study the connection between the Gromov boundary and the metric boundary.
Universal algebraic geometry allows considering of geometric properties of every universal algebra. When two algebras have same algebraic geometry? We must consider the categories of algebraic closed sets of these algebras to answer this…
We discuss some aspects of the theory of subelliptic estimates.
We introduce topological notions of normal crossings symplectic divisor and variety and establish that they are equivalent, in a suitable sense, to the desired geometric notions. Our proposed concept of equivalence of associated topological…
We give a necessary and sufficient condition for a morphism between recollements of abelian categories to be an equivalence.
In his book "Metric structures for Riemannian and non-Riemannian spaces", Gromov defined two properties of Riemannian manifolds, ellipticity and quasiregular ellipticity, and suggested that there may be a connection between the two. Since…
In the paper the main attention is paid to conditions on algebras from a given variety which provide coincidence of their algebraic geometries. The main part here play the notions mentioned in the title of the paper.
We consider the deformation theory of two kinds of geometric objects: foliations on one hand, pre-symplectic forms on the other. For each of them, we prove that the geometric notion of equivalence given by isotopies agrees with the…
The concept of Gromov hyperbolicity manifests itself in many different ways. With only mild assumptions on the underlying metric space, the spectrum of equivalent properties includes various thin triangle conditions, the stability of…