相关论文: Special lagrangian fibrations on flag variety $F^3…

In this paper we construct and classify Lagrangian T^3-fibrations on non compact symplectic manifolds with singular fibres of prescribed topological type. This contributes to the understanding of the structure of the singular fibres that…

This paper classifies Lagrangian fibrations over surfaces with compact total spaces up to fiberwise symplectomorphism identical on the base.

We construct pseudotoric structures (\`{a} la Tyurin) on the two-step flag variety $F\ell_{1, n-1; n}$, and explain a general relation between pseudotoric structures and special Lagrangian torus fibrations, the latter of which are important…

A fibration is said to be isotrivial if all of its smooth fibres are isomorphic to a single fixed variety. We classify the elliptic K3 surfaces that are isotrivial, and use them to construct Lagrangian fibrations that are isotrivial. We…

We classify lagrangian fibrations on Nikulin orbifolds, a well studied class of singular irreducible holomorphic symplectic varieties, and prove they verify the SYZ conjecture.

We prove that there are at most two possibilities for the base of a Lagrangian fibration from a complex projective irreducible symplectic fourfold.

The generic fiber of a Lagrangian fibration on an irreducible holomorphic symplectic manifold is an abelian variety. Associate a polarization type to such Lagrangian fibrations coming from polarizations on a generic fiber. We prove that…

We prove that every irreducible component of a fibre of a complex Lagrangian fibration is Lagrangian subvariety. Especially, complex Lagrangian fibations are equidimensional.

In this paper we survey some finiteness results of the deformation classes of hyperk\"ahler Lagrangian fibrations, and we prove finiteness for stable Lagrangian fibrations with a given discriminant divisor.

We explicitly construct special Lagrangian fibrations on finite quotients of maximally degenerating abelian varieties, glue with Berkovich retraction in non-Archimedean geometry by using "hybrid" technique. We also study their symmetries…

We define topological invariants of regular Lagrangian fibrations using the integral affine structure on the base space and we show that these coincide with the classes known in the literature. We also classify all symplectic types of…

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…

We construct infinitely many Legendrian links in the standard contact $\mathbb{R}^3$ with arbitrarily many topologically distinct Lagrangian fillings. The construction is used to find links in $S^3$ that bound topologically distinct pieces…

This article initiates the study of isotrivial Lagrangian fibrations of compact hyper-K\"ahler manifolds. We present four foundational results that extend well-known facts about isotrivial elliptic fibrations of K3 surfaces. First, we prove…

Given a K3 surface S, we show that the relative intermediate Jacobian of the universal family of Fano 3-folds V containing S as an anticanonical divisor is a Lagrangian fibration. The proof uses variations of the mixed Hodge structure of…

In this paper we construct all smooth torus fibres of the generalized special Lagrangian torus fibrations for Calabi-Yau hypersurfaces in toric varieties near the large complex limit.

We consider (holomorphic) Lagrangian fibrations X->P^n that satisfy some natural hypotheses. We prove that there are only finitely many such Lagrangian fibrations up to deformation.

The monodromy of almost toric Lagrangian fibrations on the complex projective plane is described.

A rational Lagrangian fibration f on an irreducible symplecitc variety V is a rational map which is birationally equivalent to a regular surjective morphism with Lagrangian fibers. By analogy with K3 surfaces, it is natural to expect that a…

We survey Lagrangian fibrations of holomorphic symplectic varieties, both compact and non-compact, whose fibres are Jacobians and Prym varieties.