Related papers: Sur la th\'eorie d'Ahlfors des surfaces
We prove the abundance theorem for semi log canonical surfaces in positive characteristic.
We present a variant of the classical Darboux-Jouanolou Theorem. Our main result provides a characterization of foliations which are pull-backs of foliations on surfaces by rational maps. As an application, we provide a structure theorem…
We prove some cycle relations on moduli of K3 surfaces
Beyond normal surfaces there are several open questions concerning 2- dimensional spaces. We present some results and conjectures along this line.
In the context of complex algebraic varieties, the decomposition theorem for semi-small maps provides a decomposition of the direct image of the constant sheaf. In this work, we develop a decomposition theorem for branched coverings of…
Some counterparts of theorems of Phragm\'en-Lindel\"of and of Ahlfors are proved for differential forms of ${\cal WT}$--classes.}
In this work we present the solution of the stellar spot problem using the Kelvin-Stokes theorem. Our result is applicable for any given location and dimension of the spots on the stellar surface. We present explicitely the result up to the…
Analysis of the Navier-Stokes equations in the frames of the algebraic approach to systems of partial differential equations (formal theory of differential equations) is presented.
The main theorem of "S. J. Kov\'acs: The cone of curves of a K3 surface, Math. Ann. 300 (1994), no. 4, 681-691" is proved in arbitrary characteristic. The proof is essentially the same as in the original paper where it was stated only over…
We prove an analog of the classical Hartogs extension theorem for CR $L^{2}$ functions defined on boundaries of certain (possibly unbounded) domains on coverings of strongly pseudoconvex manifolds. Our result is related to a problem posed…
We give conditions for a n-connective quasicoherent obstruction theory on a Deligne-Mumford stack to come from the structure of a connective spectral Deligne-Mumford stack on the underlying topos.
We give a new simpler proof of a theorem of Jayne and Rogers.
The quantum dilogarithm function of Faddeev is a special function that plays a key role as the building block of quantum invariants of knots and 3-manifolds, of quantum Teichm\"uller theory and of complex Chern-Simons theory. Motivated by…
We give a proof of the Kodaira vanishing theorem on smooth complex surfaces using geometric stability conditions. Likewise, we give a new proof of a result of Xie characterizing the counterexamples of the Kodaira vanishing theorem in…
We generalize the H. Cartan's theory of holomorphic curves for a general open Riemann surface. Besides, a vanishing theorem for jet differentials and a Bloch's theorem for Riemann surfaces are obtained.
The text deals with generalizations of the Markoff equation in number theory, arising from continued fractions. It gives the method for the complete resolution of such new equations, and their interpretation in algebra and algebraic…
We survey some aspects of the theory of elliptic surfaces and give some results aimed at determining the Picard number of such a surface. For the surfaces considered, this will be equivalent to determining the Mordell-Weil rank of an…
We extend the well-known Denjoy-Ahlfors theorem on the number of different asymptotic tracts of holomorphic functions to subharmonic functions on arbitrary Riemannian manifolds. We obtain some new versions of the Liouville theorem for…
We prove a Torelli-like theorem for higher-dimensional function fields, from the point of view of "almost-abelian" anabelian geometry.
The paper is a chapter of the above-mentioned book. It aims to give an expository presentation of author's version of the non-Abelian Stokes theorem in the framework of path-integral formalism.