相关论文: Monodromy of elliptic surfaces
Following Newton, Ivory and Arnold, we study the Newtonian potentials of algebraic hypersurfaces in $R^n$. The ramification of (analytic continuations of) these potential depends on a monodromy group, which can be considered as a proper…
In this paper, we study how certain vector bundles on an elliptic surface are changed under logarithmic transformations.
Singular fibrations generalize achiral Lefschetz fibrations of 4-manifolds over surfaces while sharing some of their properties. For instance, relatively minimal singular fibrations are determined by their monodromy. We explain how to…
We consider t-structures that naturally arise on elliptic fibrations. By filtering the category of coherent sheaves on an elliptic fibration using the torsion pairs corresponding to these t-structures, we prove results describing…
This paper is the first in a series of three papers concerning the surface T times T. In this paper we study the degeneration of T times T and the regeneration of its degenerated object. We study the braid monodromy and its regeneration.
Atiyah classifies vector bundles on elliptic curves $E$ over an algebraically closed field of any characteristic. On the other hand, a rank $2$ vector bundle on $E$ defines a surface $S$ with a $\mathbb{P}^1$-bundle structure on $E$. We…
A central role in recent investigations of the duality of F-theory and heterotic strings is played by the moduli of principal bundles, with various structure groups G, over an elliptically fibered Calabi-Yau manifold on which the heterotic…
We classify subgroups of $\textrm{SL}(2,\mathbb{Z})$ up to conjugacy, which occur as monodromy groups of elliptically fibered K3 surfaces following a general strategy proposed by Bogomolov and Tschinkel. The essential step is the…
Let X->P^(n-1) be an elliptic fibration obtained by resolving the indeterminacy of the projection of a cubic hypersurface Y of P^(n+1) from a line L not contained in Y. We prove that the Mordell-Weil group of the elliptic fibration is…
We exhibit low-dilatation families of surface homeomorphisms among monodromies of Lorenz knots.
We study relatively minimal surfaces equipped with a strongly isotrivial elliptic fibration in positive characteristic by means of the notion of equivariantly normal curves introduced and developed recently by Brion. Such surfaces are…
Following T. Suwa, we study unfoldings of algebraic foliations and their relationship with families of foliations, making focus on those unfoldings related to trivial families. The results obtained in the study of unfoldings are then…
We construct pairs of elliptic curves over number fields with large intersection of projective torsion points.
We use pluriharmonic maps to study representations of fundamental groups of algebraic manifolds. This approach is functorial in the sense that the restriction of such a map to a fiber of a fibration remains pluriharmonic, and on this basis,…
The supersingular K3 surface X in characteristic 2 with Artin invariant 1 admits several genus 1 fibrations (elliptic and quasi-elliptic). We use a bijection between fibrations and definite even lattices of rank 20 and discriminant 4 to…
We compute Mordell-Weil groups for extremal semistable elliptic fibrations of K3 surfaces
We study the homotopy groups of generic leaves of logarithmic foliations on complex projective manifolds. We exhibit a relation between the homotopy groups of a generic leaf and of the complement of the polar divisor of the logarithmic…
We survey on algebraically elliptic varieties in the sense of Gromov.
We construct three new families of fibrations $\pi : S \to B$ where $S$ is an algebraic complex surface and $B$ a curve that violate Xiao's conjecture relating the relative irregularity and the genus of the general fiber. The fibers of…
Layered monoidal theories provide a categorical framework for studying scientific theories at different levels of abstraction, via string diagrammatic algebra. We introduce models for three closely related classes of layered monoidal…