Related papers: Multiple fibers of holomorphic Lagrangian fibratio…

We prove that a terminal three-dimensional del Pezzo fibration has no fibers of multiplicity $\ge 6$. We also obtain a rough classification possible configurations of singular points on multiple fibers and give some examples.

In this note, we verify that the complex Kodaira dimension $\kappa^h$ equals the symplectic Kodaira dimension $\kappa^s$ for smooth 4-manifolds with complex and symplectic structures. We also calculate the Kodaira dimension for many…

We present two methods for studying fibrations of Calabi-Yau manifolds embedded in toric varieties described by single weight systems. We analyse 184,026 such spaces and identify among them 124,701 which are K3 fibrations. As some of the…

We find through a systematic analysis that all but 29,223 of the 473.8 million 4D reflexive polytopes found by Kreuzer and Skarke have a 2D reflexive subpolytope. Such a subpolytope is generally associated with the presence of an elliptic…

Given a positive singular hermitian metric of a pseudoeffective line bundle on a complex Kaehler manifold, a singular foliation is constructed satisfying certain analytic analogues of numerical conditions. This foliation refines Tsuji's…

Given a family of varieties over the projective line, we study the density of fibres that are everywhere locally soluble in the case that components of higher multiplicity are allowed. We use log geometry to formulate a new sparsity…

In this note we define fibrations of topological stacks and establish their main properties. We prove various standard results about fibrations (fiber homotopy exact sequence, Leray-Serre and Eilenberg-Moore spectral sequences, etc.). We…

Barth and Peters showed that a general complex Enriques surface has exactly 527 isomorphism classes of elliptic fibrations. We show that every Enriques surface has precisely 527 isomorphism classes of elliptic fibrations when counted with…

Using Lagrangian Floer theory, we study the tropical geometry of K3 surfaces with general singular fibres. In particular, we give the local models for the type $I_n$, $II$, $III$ and $IV$ singular fibres in the Kodaira's classification and…

This paper completes the classification of regular Lagrangian fibratiopns over compact surfaces. \cite{misha} classifies regular Lagrangian fibrations over $\mathbb{T}^2$. The main theorem in \cite{hirsch} is used in order to classify…

We discuss a notion of large complex structure for elliptic K3 surfaces with section inspired by the eight-dimensional F-theory/heterotic duality in string theory. This concept is naturally associated with the Type II Mumford partial…

Let $X$ be a hyperk\"ahler variety admitting a Lagrangian fibration. Beauville's "splitting property" conjecture predicts that fibres of the Lagrangian fibration should have a particular behaviour in the Chow ring of $X$. We study this…

We investigate fibrations by non-hyperelliptic curves of arithmetic genus three and geometric genus one in characteristic two. Assuming that there is only one moving singularity and that its image in the Frobenius pullback of the fibration…

We show that if $X$ is a smooth complex projective variety with Kodaira dimension $0$ then the Kodaira dimension of a general fiber of its Albanese map is at most $h^0(\Omega ^1 _X)$.

We prove an additivity result for the log Kodaira dimension of algebraic fiber spaces over abelian varieties, a superadditivity result for fiber spaces over varieties of maximal Albanese dimension, as well as a subadditivity result for log…

We describe all the elliptic fibrations with section on the Kummer surface X of the Jacobian of a very general curve C of genus 2 over an algebraically closed field of characteristic 0, modulo the automorphism group of X and the symmetric…

We study the Lagrangian isotopy classification of Lagrangian spheres in the Milnor fibre, $B_{d,p,q}$, of the cyclic quotient surface T-singularity $\frac{1}{dp^2} (1,dpq-1)$. We prove that there is a finitely generated group of…

We classify all Jacobian elliptic fibrations on K3 surfaces with finite automorphism group. We also classify all Jacobian elliptic fibrations with finite Mordell-Weil group on K3 surfaces with infinite automorphism group and 2-elementary…

Let $X$ be a hyperk\"ahler variety, and let $Z\subset X$ be a Lagrangian subvariety. Conjecturally, $Z$ should have trivial intersection with certain parts of the Chow ring of $X$. We prove this conjecture for certain Hilbert schemes $X$…

For a Zariski general (regular) hypersurface $V$ of degree $M$ in the $(M+1)$-dimensional projective space, where $M$ is at least 16, with at most quadratic singularities of rank at least 13, we give a complete description of the structures…