arXiv research

Singular fibrations over surfaces generalize Lefschetz fibrations and have new construction methods.

Study how singular fibrations affect Poisson cohomology in 4D.

Study on conditions for singular local tube fibrations.

Introduces new stability concept for Fano fibrations.

Study singular fibers in genus 2 algebraic fibrations and their monodromy factorizations.

Third in a series, this paper constructs non-trivial Cayley fibrations with conical singularities.

Study fibrations over $S^2$ with same singularities, showing monodromies are equivalent up to direct sums.

New singularities and fibrations in non-orientable 4-manifolds.

Builds torus fibrations over singular manifolds with specific features.

Minimal singular fibers found in nonorientable Lefschetz fibrations.

Study on hyperelliptic Lefschetz fibrations, finding singular fiber counts.

Uniform diameter bounds for Calabi-Yau fibrations with singular fibers.

Milnor fibrations were extended by Mutsuo Oka for certain mixed polynomial. In this paper, we study singular points of differentiable maps into the 2-dimensional torus, called Milnor fibration product maps, obtained by several Milnor fibrations for mixed polynomial. We give a characterization of singular points of such…

Milnor fibrations have been studied since 1960's. In this paper, we study singular points of differentiable maps, called Milnor fibration product maps, obtained by several Milnor fibrations. We give a characterization of singular points of such product maps, and for the case of certain weighted homogeneous polynomials,…

In the paper we introduce the notions of a singular fibration and a singular Seifert fibration. These notions are natural generalizations of the notion of a locally trivial fibration to the category of stratified pseudomanifolds. For singular foliations defined by such fibrations we prove a de Rham type theorem for the…

This paper extends previous work on genus two fibrations by studying and resolving singular fibers.

Study shows Lefschetz fibrations on Milnor fibers of certain singularities.

The paper connects fibrations to generalized complex structures in semi-toric geometry.

Extends Serre-Swan theorem to all finitely generated modules over smooth functions.

Constructs Lefschetz fibrations on exotic 4-manifolds, providing bounds and equalities for singular fibers.

We prove that a Lefschetz fibration over the disc that, after compactification, has the same singular fibers as an extremal rational elliptic surface can be obtained by deleting a singular fiber and a section from the rational extremal elliptic surface, i.e. such a Lefschetz fibration is determined up to topological eq…

In this note we show that if a compact Kahler manifold with trivial canonical bundle is the total space of a holomorphic fibration without singular fibers, then the fibration is a holomorphic fiber bundle. In the algebraic case, the fibration becomes trivial after a finite base change.

Study on four-dimensional Dehn twists and Milnor fibrations, revealing new phenomena.

New maps show some surfaces can't be sections of 4D spheres.

Given some type of fibration on a 4-manifold $X$ with a torus regular fiber $T$, we may produce a new 4-manifold $X_T$ by performing torus surgery on $T$. There is a natural way to extend the fibration to $X_T$, but a multiple fiber (non-generic) singularity is introduced. We construct explicit generic fibrations (with…

Survey uses Milnor fibrations to classify first integrals of differential systems.

Generalizes Lefschetz fibrations with rational homology disk smoothings.

Deformations of singular Cayley submanifolds studied.

Using the recent results of Siebert and Tian about the holomorphicity of genus 2 Lefschetz fibrations with irreducible singular fibers, we show that any genus 2 Lefschetz fibration becomes holomorphic after fiber sum with a holomorphic fibration.

Model for associative submanifolds in K3 fibrations.

We construct universal Lefschetz fibrations, defined in analogy with classical universal bundles. We also introduce the cobordism groups of Lefschetz fibrations, and we see how these groups are quotients of the singular bordism groups via the universal Lefschetz fibrations.

Study Fano fibrations and Kähler-Ricci flow singularities, proving diameter bounds and curvature estimates.

We construct examples of Lefschetz fibrations with prescribed singular fibers. By taking differences of pairs of such fibrations with the same singular fibers, we obtain new examples of surface bundles over surfaces with non-zero signature. From these we derive new upper bounds for the minimal genus of a surface repres…

We are going to use the Euler's vector fields in order to show that for real quasi-homogeneous singularities with isolated critical value, the Milnor's fibration in a "thin" hollowed tube involving the zero level and the fibration in the complement of "link" in sphere are equivalents, since they exist. Moreover, in ord…

New solutions found for $G_2$ system using K3 orbifolds.

Study symplectic fillings of sandwiched singularities.

Study finds negatively curved spheres in elliptic surfaces and their modifications.

We explore a number of examples of special Lagrangian fibrations on non-compact Calabi-Yau manifolds invariant under torus actions. These include fibrations on crepant resolutions of canonical toric singularities (already found by Goldstein), proper versions of these fibrations, and fibrations on flat deformations of c…

The paper proves a precise SYZ conjecture for toric Calabi-Yau manifolds with singular fibers.

We compute the formal Poisson cohomology of a broken Lefschetz fibration by calculating it at fold and Lefschetz singularities. Near a fold singularity the computation reduces to that for a point singularity in 3 dimensions. For the Poisson cohomology around singular points we adapt techniques developed for the Sklyani…

The SYZ Conjecture explains Mirror Symmetry between mirror Calabi-Yau 3-folds M,M' in terms of special Lagrangian fibrations f : M --> B and f' : M' --> B over the same base B, whose fibres are dual 3-tori, except for singular fibres. One of the main problems in proving the SYZ Conjecture (or even in finding the right …

We introduce the $2$-nodal spherical deformation of certain singular fibers of genus $2$ fibrations, and use such deformations to construct various examples of simply connected minimal symplectic $4$-manifolds with small topology. More specifically, we construct new exotic minimal symplectic $4$-manifolds homeomorphic …

New method normalizes Milnor fibrations for real analytic maps.

We show that generalized broken fibrations in arbitrary dimensions admit rank-2 Poisson structures compatible with the fibration structure. After extending the notion of wrinkled fibration to dimension 6 we prove that these wrinkled fibrations also admit compatible rank-2 Poisson structures. In the cases with indefinit…

Bryant-Salamon constructed three 1-parameter families of complete manifolds with holonomy $\mathrm{G}_2$ which are asymptotically conical to a holonomy $\mathrm{G}_2$ cone. For each of these families, including their asymptotic cone, we construct a fibration by asymptotically conical and conically singular coassociativ…

Paper proves direct image sheaf positivity for certain Kähler fibrations.

In this article, we construct a genus-$0$ or genus-$1$ positive allowable Lefschetz fibration on any minimal symplectic filling of the link of non-cyclic quotient surface singularities. As a byproduct, we also show that any minimal symplectic filling of the link of quotient surface singularities can be obtained from a …

In this paper we give a construction of Lagrangian torus fibration for Calabi-Yau hypersurface in toric variety via the method of gradient flow. Using our construction of Lagrangian torus fibration, we are able to prove the symplectic topological version of SYZ mirror conjecture for generic Calabi-Yau hypersurface in t…