Related papers: An integrable system of K3-Fano flags

Over an algebraically closed field of positive characteristic, we classify smooth Fano threefolds of Picard number one whose anti-canonical linear systems are not very ample. Furthermore, we also prove that an anti-canonically embedded Fano…

We classify complex K3 surfaces of zero entropy admitting an elliptic fibration with only irreducible fibers. These surfaces are characterized by the fact that they admit a unique elliptic fibration with infinite automorphism group. We…

In a Type III degeneration of K3-surfaces the dual graph of the central fibre is a triangulation of the 2-sphere. We realise the tetrahedral, octahedral and especially the icosahedral triangulation in families of K3-surfaces, preferably…

We classify the irreducible components of the space of foliations on Fano 3-folds with rank one Picard group. As a corollary we obtain a classification of holomorphic Poisson structures on the same class of 3-folds.

We prove that every smooth Fano threefold from the family No 2.8 is K-stable. Such a Fano threefold is a double cover of the blow-up of $\mathbb{P}^3$ at one point branched along an anti-canonical divisor.

In this paper we study embeddings of oriented connected closed surfaces in $\mathbb S^3$. We define a complete invariant, the fundamental span, for such embeddings, generalizing the notion of the peripheral system of a knot group. From the…

We study elliptically fibered K3 surfaces, with sections, in toric Fano threefolds which satisfy certain combinatorial properties relevant to F-theory/Heterotic duality. We show that some of these conditions are equivalent to the existence…

We study the K-stability of singular Fano 3-folds with canonical Gorenstein singularities whose anticanonical linear system is base-point-free but not very ample.

We generalize the equivariant intermediate Jacobian torsor obstruction over $\mathbb{C}$ to algebraically closed fields of characteristic zero. It is an obstruction to the (projective) linearizability problem of finite group actions on…

This is the sixth in a series of papers constructing examples of special Lagrangian m-folds in C^m. We present a construction of special Lagrangian cones in C^3 involving two commuting o.d.e.s, motivated by the first two papers of the…

We show several examples of integrable systems related to special K3 and rational surfaces (e.g., an elliptic K3 surface, a K3 surface given by a double covering of the projective plane, a rational elliptic surface, etc.). The construction,…

Filip showed that there are constants $C>0$ and $\delta>0$ such that the number of special Lagrangian fibrations of volume $\leq V$ in a generic twistor family of K3 surfaces is $C\cdot V^{20}+O(V^{20-\delta})$. In this note, we show that…

Markushevich and Tikhomirov provided a construction of an irreducible symplectic V-manifold of dimension 4, the relative compactified Prym variety of a family of curves with involution, which is a Lagrangian fibration with polarization of…

We investigate when the fundamental group of the smooth part of a K3 surface or Enriques surface with Du Val singularities, is finite. As a corollary we give an effective upper bound for the order of the fundamental group of the smooth part…

In arXiv:2409.03960, we introduced an approach to the question of extendability of projective varieties via degeneration to ribbons. In this article we build on these methods to give a new proof of optimal results on the extendability of…

We give a method to construct singular Lagrangian 3-torus fibrations over certain a priori given integral affine manifolds with singularities, which we call simple. The main result of this article is the proof that the topological…

We show boundedness of $3$-folds of $\epsilon$-Fano type with Mori fibration structures. The proof is based on the birational boundedness result in our previous work arXiv:1509.08722 combining with arguments in Kawamata \cite{K} and…

For a $\mathbb{Q}$-Fano 3-fold $X$ on which $K_X$ is a canonical divisor, we investigate the geometry induced from the linear system $|-mK_X|$ in this paper and prove that the anti-$m$-canonical map $\varphi_{-m}$ is birational onto its…

The Ap\'ery numbers of Fano varieties are asymptotic invariants of their quantum differential equations. In this paper, we initiate a program to exhibit these invariants as (mirror to) limiting extension classes of higher cycles on the…

We consider K3 surfaces which are double cover of rational elliptic surfaces. The former are endowed with a natural elliptic fibration, which is induced by the latter. There are also other elliptic fibrations on such K3 surfaces, which are…