arXiv research

A study on the relation between the smooth structure of a symplectic homotopy K3 surface and its symplectic symmetries is initiated. A measurement of exoticness of a symplectic homotopy K3 surface is introduced, and the influence of an effective action of a K3 group via symplectic symmetries is investigated. It is show…

Study on automorphisms of K3 and Enriques surfaces, proving entropy gaps and achirality.

Study K3 surfaces and their metrics, focusing on dynamics.

Study on K3 surfaces' collapsing and special Kähler structures.

Compactifies metrics on K3 surfaces with algebraic description.

We will show the following three theorems on the diffeomorphism and homeomorphism groups of a $K3$ surface. The first theorem is that the natural map $π_{0}(Diff(K3)) \to Aut(H^{2}(K3;\mathbb{Z}))$ has a section over its image. The second is that, there exists a subgroup $G$ of $π_{0}(Diff(K3))$ of order two over which…

Simply connected moduli space of Ricci flat metrics on K3 surfaces.

The study of special Lagrangian classes and semistable Mukai vectors on K3 surfaces.

Study geometric quantization on K3 surfaces, showing spectral convergence.

Researchers found non-smoothable surfaces in a 4-sphere, solving K3 problems.

Boundary Dehn twist on $K3$ surfaces becomes trivial after abelianization.

Study describes limits of non-collapsing K3 surfaces using algebraic data.

Constructs entropy-minimizing pseudo-Anosov diffeomorphisms on K3 surfaces.

Researchers find geodesics on K3 surfaces using electrostatics.

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

Constructs currents and heights on K3 surfaces.

Special Lagrangian submanifolds emerge from K3 surface collapse.

We show that for complex analytic K3 surfaces any torsion class in H^2(X,O_X^*) comes from an Azumaya algebra. In other words, the Brauer group equals the cohomological Brauer group. For algebraic surfaces, such results go back to Grothendieck. In our situation, we use twistor spaces to deform a given analytic K3 surfa…

Study shows symplectic mapping groups of K3 surfaces are infinitely generated.

Study connects K3 surfaces to holomorphic metrics, solving complex structure variation.

Generalized Calabi-Yau structures, a notion recently introduced by Hitchin, are studied in the case of K3 surfaces. We show how they are related to the classical theory of K3 surfaces and to moduli spaces of certain SCFT as studied by Aspinwall and Morrison. It turns out that K3 surfaces and symplectic structures are b…

The aim of this paper is to show the rigidity of homologically trivial actions of prime order on K3 surfaces. To be precise, we show that homotopy K3 surfaces do not admit a periodic diffeomorphism of odd prime order 3 acting trivially on cohomology. Moreover, we give an obstruction in terms of the rationality and sign…

Study on energy of maps from K3 surface to flat orbifold.

Study shows K-moduli spaces connect quartic surfaces to K3 surfaces, verifying predictions and classifying degenerations.

In this paper, we give a weak classification of locally linear pseudofree actions of the cyclic group of order 3 on a $K3$ surface, and prove the existence of such an action which can not be realized as a smooth action on the standard smooth $K3$ surface.

We compute the genus zero family Gromov-Witten invariants for K3 surfaces using the topological recursion formula and the symplectic sum formula for a degeneration of elliptic K3 surfaces. In particular we verify the Yau-Zaslow formula for non-primitive classes of index two.

We study K3 surfaces with a pair of commuting involutions that are non-symplectic with respect to two anti-commuting complex structures that are determined by a hyper-Kähler metric. One motivation for this paper is the role of such $\mathbb{Z}^2_2$-actions for the construction of $G_2$-manifolds. We find a large class …

Simplified proof of K3 surface period map surjectivity.

This paper treats the theory of Mukai duality on K3 surfaces from the differential geometric perspective, taylored to the need of the author's companion paper about Mukai duality of adiabatic coassociative K3 fibrations.

The paper proves geometrical finiteness for automorphism groups of K3 surfaces and related varieties.

Study geodesics on K3 surfaces near orbifold limit.

We exhibit families of Ricci-flat Kahler metrics on K3 surfaces which collapse to an interval, with Tian-Yau and Taub-NUT metrics occurring as bubbles. There is a corresponding continuous surjective map from the K3 surface to the interval, with regular fibers diffeomorphic to either 3-tori or Heisenberg nilmanifolds.

The study finds families of surfaces with specific properties and connects them to rational curve configurations in K3 surfaces.

New K3 surfaces with two involutions and low Picard number constructed.

Stability conditions on K3 surfaces are linked to the masses of spherical objects.

Study shows complex K3 surfaces have infinite free abelian subgroup in their diffeomorphism group.

We study the decomposability of a Lagrangian homology class on a K3 surface into a sum of classes represented by special Lagrangian submanifolds, and develop criteria for it in terms of lattice theory. As a result, we prove the decomposability on an arbitrary K3 surface with respect to the Kähler classes in dense subse…

Study Dehn-Seidel twists on Lagrangian spheres in K3 surfaces.

We give a systematic method to calculate some homological data from the global monodromy of a topological elliptic surface. We apply this method to the cases 1) the transcendental lattice of an extremal elliptic K3 surface, 2) the torsion part of Mordell-Weil group of a general elliptic surface, and 3) the Mordell-Weil…

Researchers prove smoothings for surfaces with triple points.

All knots with unknotting number ≤ 21 are smoothly slice in K3 surface.

New geometric examples of involutions on Hilbert square K3 surfaces.

Constructs stable bundles on K3 surfaces using monad construction.

Nontrivial boundary Dehn twist found on K3#K3 manifold.

We give an alternative proof of a result of Cantat and Dupont, showing that any automorphism of a K3 surface with measure of maximal entropy in the Lebesgue class must be a Kummer example. Our method exploits the existence of Ricci-flat metrics on K3s and also covers the non-projective case.

The paper solves a geometric problem related to K3 surfaces and complex-hyperkähler metrics.

We prove that any weakly triholomorphic map from a compact hyperkähler surface to an algebraic K3 surface defined by a homogeneous polynomial of degree 4 in $\mathbb{C}P^3$ has only isolated singularities.

We complete the remaining cases of the conjecture predicting existence of infinitely many rational curves on K3 surfaces in characteristic zero, prove almost all cases in positive characteristic and improve the proofs of the previously known cases. To achieve this, we introduce two new techniques in the deformation the…