Related papers: Cubic fourfolds, Kuznetsov components and Chow mot…

We construct an isomorphism of graded Frobenius algebras between the orbifold Chow ring of weighted projective spaces and graded algebras of groups of roots of the unity.

We give counting formulas for the number of Fourier-Mukai partners of the K3 category of a very general special cubic fourfold.

A Frobenius manifold has tri-hamiltonian structure if it is even-dimensional and its spectrum is maximally degenerate. We focus on the case of dimension four and show that, under the assumption of semisimplicity, the corresponding…

Let $k$ be a perfect field and $X$ be a smooth projective surface over $k$ with a rational point, we discuss the condition of splitting off the top cell for the motivic stable homotopy type of $X$. We also study some outlying examples, such…

We discuss the structure of the derived category of coherent sheaves on cubic fourfolds of three types: Pfaffian cubics, cubics containing a plane and singular cubics, and discuss its relation to the rationality of these cubics.

We show that any orientation preserving Hodge isometry between the Hodge structures of two K3 surfaces X and X' twisted by Brauer classes $\alpha$ resp. $\alpha'$ can be lifted to a Fourier-Mukai equivalence between the derived categories…

We study the Chow motive (with rational coefficients) of a hypersurface X in the projective space by using the variety F(X) of l-dimensional planes contained in X. If the degree of X is sufficiently small we show that the primitive part of…

Given a semisimple Frobenius manifold, we construct a class of integrable deformations of its hierarchy of topological type. We show that these integrable deformations have polynomial tau-structures, and conjecture that for the…

We construct singular quartic double fivefolds whose Kuznetsov component admits a crepant categorical resolution of singularities by a twisted Calabi--Yau threefold. We also construct rational specializations of these fivefolds where such a…

We prove that there exists a one-to-one correspondence between smooth quartic surfaces with an outer Galois point and K3 surfaces with a certain automorphism of order 4. Furthermore, we characterize quartic surfaces with two or more outer…

We present a detailed study of elliptic fibrations on Fourier-Mukai partners of K3 surfaces, which we call derived elliptic structures. We fully classify derived elliptic structures in terms of Hodge-theoretic data, similar to the Derived…

We carry out the explicit computations that are used to write down the integrable hierarchy associated with the quintic Calabi-Yau threefold. We also do the calculations for the geometric structures emerging in the Gromov-Witten theory of…

We exhibit basic algebro-geometric results on the formal model of semi-infinite flag varieties and its Schubert varieties over an algebraically closed field $\mathbb K$ of characteristic $\neq 2$ from scratch. We show that the formal model…

In this paper we show that the moduli space of nodal cubic surfaces is isomorphic to a quotient of a 4-dimensional complex ball by an arithmetic subgroup of the unitary group. This complex ball uniformization uses the periods of certain K3…

We provide a new $L^2$-Hodge theoretic construction of a Frobenius manifold structure on the cohomology of a Calabi-Yau smooth projective hypersurface $V$, using Li-Wen's $L^2$-Hodge theory [9] of a Landau-Ginzburg model with compact…

A generalized Kummer surface $X$ of order $3$ is the minimal resolution of the quotient of an abelian surface $A$ by an order $3$ symplectic automorphism. We study a generalization of a problem of Shioda for classical Kummer surfaces, which…

We characterize the subscheme of the moduli space of torsion-free sheaves on an elliptic surface which are stable of relative degree zeero (with respect to a polarization of type aH+bf, H being the section and f the elliptic fibre) which is…

In this article we introduce the local versions of the Voevodsky category of motives with Z/p-coefficients over a field k, parameterized by finitely-generated extensions of k. We introduce the, so-called, flexible fields, passage to which…

This is a survey article on mirror symmetry and Fourier-Mukai partners of Calabi-Yau threefolds with Picard number one based on recent works by the authors [HoTa1,2,3,4]. For completeness, mirror symmetry and Fourier-Mukai partners of K3…

In this note, we generalize results of Donagi and Pantev on twisted derived equivalences between elliptically fibered surfaces to higher dimensions. First, we establish a twisted derived equivalence between torsors under abelian schemes…