Finiteness of semialgebraic types of polynomial functions.
Finiteness problem for meromorphic mappings sharing n+3 hyperplanes of ℙⁿ(ℂ)
We prove some finiteness theorems for differential nondegenerate meromorphic mappings of into ℙⁿ(ℂ) which share n+3 hyperplanes.
Finiteness problems on Nash manifolds and Nash sets
We study here several finiteness problems concerning affine Nash manifolds and Nash subsets . Three main results are: (i) A Nash function on a semialgebraic subset of has a Nash extension to an open semialgebraic neighborhood of in , (ii) A Nash set that has only normal crossings in can be covered by finitely many open semialgebraic sets equipped with Nash diffeomorphisms such that , (iii) Every affine Nash manifold with corners is a closed subset of an affine Nash manifold...
Finiteness property for generalized abelian integrals
We study the integrals of real functions which are finite compositions of globally subanalytic maps and real power functions. These functions have finiteness properties very similar to those of subanalytic functions. Our aim is to investigate how such finiteness properties can remain when taking the integrals of such functions. The main result is that for almost all power maps arising in a -function, its integration leads to a non-oscillating function. This can be seen as a generalization of Varchenko...
Finiteness Results for Algebraic K3 Surfaces.
Finiteness results for Teichmüller curves
We show that for each genus there are only finitely many algebraically primitive Teichmüller curves , such that (i) lies in the hyperelliptic locus and (ii) is generated by an abelian differential with two zeros of order . We prove moreover that for these Teichmüller curves the trace field of the affine group is not only totally real but cyclotomic.
Finiteness theorems for the cohomology of an overconvergent isocrystal on a curve
Finite-type invariants of Legendrian knots in the 3-space: Maslov index as an order 1 invariant
We consider a contractible closure of the space of Legendrian knots in the standard contact 3-space. We show that in this context the space of finite-type complex-valued invariants of Legendrian knots is isomorphic to that of framed knots in with an extra order 1 generator (Maslov index) added.
Finsler Structures of Negative Curvature in ...-Linear Fibre Spaces.
First Order Completeness Theorems.
Fixed points for automorphisms in Cartan domains of type IV
Fixpunktmengen kompakter Gruppen in Teilgebieten Steinscher Mannigfaltigkeiten.
Flabbiness for solution sheaves of microdifferential systems
Flag Structures on Seifert Manifolds.
Flatness testing over singular bases
We show that non-flatness of a morphism φ:X→ Y of complex-analytic spaces with a locally irreducible target of dimension n manifests in the existence of vertical components in the n-fold fibred power of the pull-back of φ to the desingularization of Y. An algebraic analogue follows: Let R be a locally (analytically) irreducible finite type ℂ-algebra and an integral domain of Krull dimension n, and let S be a regular n-dimensional algebra of finite type over R (but not necessarily a finite R-module),...
Foliated structure of the Kuranishi space and isomorphisms of deformation families of compact complex manifolds
Consider the following uniformization problem. Take two holomorphic (parametrized by some analytic set defined on a neighborhood of in , for some ) or differentiable (parametrized by an open neighborhood of in , for some ) deformation families of compact complex manifolds. Assume they are pointwise isomorphic, that is for each point of the parameter space, the fiber over of the first family is biholomorphic to the fiber over of the second family. Then, under which conditions are the...
Foliations and the generalized complex Monge-Ampère equations
Foliations by complex manifolds involving the complex Hessian [Book]
Foliations by curves with curves as singularities
Let be a holomorphic one-dimensional foliation on such that the components of its singular locus are curves and points . We determine the number of , counted with multiplicities, in terms of invariants of and , assuming that is special along the . Allowing just one nonzero dimensional component on , we also prove results on when the foliation happens to be determined by its singular locus.
Foliations in algebraic surfaces having a rational first integral.
Given a foliation F in an algebraic surface having a rational first integral a genus formula for the general solution is obtained. In the case S = P2 some new counter-examples to the classic formulation of the Poincaré problem are presented. If S is a rational surface and F has singularities of type (1, 1) or (1,-1) we prove that the general solution is a non-singular curve.