Related papers: Spherical functors on the Kummer surface
In this paper we study the automorphisms group of some $K3$ surfaces which are double covers of the projective plane ramified over a smooth sextic plane curve. More precisely, we study the case of a $K3$ surface of Picard rank two such that…
We study isogeny relations between K3 surfaces and Kummer surfaces. Specifically, we prove a Torelli-type theorem for the existence of rational maps from K3 surfaces to Kummer surfaces, and a Kummer sandwich theorem for K3 surfaces with…
McMullen proved that there exists an automorphism of minimal topological entropy on a projective K3 surface. We derive equations for the surface and its automorphism. We reconstruct the surface and its automorphism from the Hodge theoretic…
We apply our earlier results on Fourier-Mukai partners to answer definitively a question about Kummer surface structures, posed by T. Shioda 25 years ago.
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…
In this article, we study complete surfaces $\Sigma$, isometrically immersed in the product space $\mathbb{H}^2\times\mathbb{R}$ or $\mathbb{S}^2\times\mathbb{R}$ having positive extrinsic curvature $K_e$. Let $K_i$ denote the intrinsic…
In this short note we observe that, for purely formal reasons, any autoequivalence can be constructed as a twist around a spherical functor. As an example, we show how the P-twists constructed by Huybrechts and Thomas can be formulated as…
In this note we interpret a recent result of Gaberdiel, Hohenegger and Volpato in terms of derived equivalences of K3 surfaces. We prove that there is a natural bijection between subgroups of the Conway group Co_1 with invariant lattice of…
We describe the equations and Gr\"obner bases of some degenerate K3 surfaces associated to rational normal scrolls. These K3 surfaces are members of a class of interesting singular projective varieties we call correspondence scrolls. The…
Motivated by the study of the growth rate of the number of geodesics in flat surfaces with bounded lengths, we study generalizations of such problems for K3 surfaces. In one generalization, we give a result regarding the upper bound on the…
Smooth K-functors are introduced and the smooth K-theory of locally convex algebras is developed. It is proved that the algebraic and smooth K-functors are isomorphic on the category of quasi stable real (or complex) Frechet algebras.
In this paper we study Seidel's mirror map for abelian and Kummer surfaces. We find that mirror symmetry leads in a very natural way to the classical parametrization of Kummer surfaces in $\P^3$. Moreover, we describe a family of embeddings…
E. Segal proved that any autoequivalence of an enhanced triangulated category can be realised as a spherical twist. However, when exhibiting an autoequivalence as a spherical twist one has various choices for the source category of the…
This paper constructs derived autoequivalences of Gorenstein orders as twists around spherical functors. More precisely, given a Gorenstein order $A$ and a quotient $p \colon A \to B$, then we specify natural conditions on $B$ under which…
We introduce a periodic form of the iterated algebraic K-theory of ku, the (connective) complex K-theory spectrum, as well as a natural twisting of this cohomology theory by higher gerbes. Furthermore, we prove a form of topological…
Every indefinite binary form occurs as the Picard lattice of some K3-surface. The group of its isometries, or automorphs, coincides with the automorphism group of the K3-surface, but only up to finite groups. The classical theory of…
We consider 2-surfaces arising from the Korteweg de Vries (KdV) equation. The surfaces corresponding to KdV are in a three dimensional Minkowski space. They contain a family of quadratic Weingarten and Willmore-like surfaces. We show that a…
We examine the proposal made recently that the su(3) modular invariant partition functions could be related to the geometry of the complex Fermat curves. Although a number of coincidences and similarities emerge between them and certain…
In this paper, we give an example of an autoequivalence with positive categorical entropy (in the sense of Dimitrov, Haiden, Katzarkov and Kontsevich) for any surface containing a (-2)-curve. Then we show that this equivalence gives another…
We study the geometry of exceptional loci of birational contractions of hyper-K\"ahler fourfolds that are of K3$^{[2]}$-type. These loci are conic bundles over K3 surfaces and we determine their classes in the Brauer group. For this we use…