Related papers: Categorical entropy for Fourier-Mukai transforms o…
We give a classification of maximal elements of the set of finite groups that can be realized as the full automorphism groups of polarized abelian surfaces over finite fields.
We determine endomorphism algebras of abelian surfaces with quaternion multiplication.
We present an algorithm to compute the automorphism group of a Mori dream space. As an example calculation, we determine the automorphism groups of singular cubic surfaces with general parameters. The strategy is to study graded…
We study twisted ideal sheaves of small length on an irreducible principally polarized abelian surface (T,l). Using Fourier-Mukai techniques we associate certain jumping schemes to such sheaves and completely classify such loci. We give…
We characterize simple complex abelian varieties and simple abelian surfaces in terms of primitivity of translation automorphisms. Applying this together with a result due to Diller and Favre, we then classify all primitive birational…
We classify smooth projective surfaces that are quotients of abelian surfaces by finite groups.
We describe the group of exact autoequivalences of the bounded derived category of coherent sheaves on a bielliptic surface. We achieve this by studying its action on the numerical Grothendieck group of the surface.
To answer a question about the distribution of products of elliptic curves in isogeny classes of abelian surfaces defined over finite fields, we compute specific orbital integrals in the group $\mathrm{GSp}_4$. More precisely, we compute…
We give a formula for the specialization of the Fourier-Mukai transform on a semi-abelian variety of torus rank 1.
We construct the Fukaya category of a closed surface equipped with an area form using only elementary (essentially combinatorial) methods. We also compute the Grothendieck group of its derived category.
This article is based on a talk given at the Kinosaki Symposium on Algebraic Geometry in 2015, about a work in progress. We describe a polarization on a derived equivalent abelian variety by using Fourier-Mukai theory. We explicitly…
Consider a quartic $q$-Weil polynomial $f$. Motivated by equidistribution considerations we define, for each prime $\ell$, a local factor which measures the relative frequency with which $f\bmod \ell$ occurs as the characteristic polynomial…
We classify two-dimensional complex tori admitting automorphisms with positive entropy in terms of the entropies they exhibit. For each possible positive value of entropy, we describe the set of two-dimensional complex tori admitting…
In this paper, we prove a refinement of the Katsura theorem on finite group actions on abelian surfaces such that the quotient is birational to a $K3$ surface. As an application, we compute traces of Frobenius on the Neron--Severi groups of…
We give a classification of all principally polarized abelian surfaces that admit an $(l,l)$-isogeny to themselves, and show how to compute all the abelian surfaces that occur. We make the classification explicit in the simplest case $l=2$.…
In this article, we study the $G$-autoequivalences of the derived category $\mathbf{D}^b_G(A)$ of $G$-equivariant objects for an abelian variety $A$ with $G$ being a finite subgroup of $\mathrm{Pic}^0(A)$. We provide a result analogue to…
We calculate the automorphism group of the generic quantum grassmannian.
We classify complex projective surfaces with an automorphism of positive entropy for which the unique invariant measure of maximal entropy is absolutely continuous with respect to Lebesgue measure.
We compute the generic degrees of the Ariki--Koike algebras by first constructing a basis of matrix units in the semisimple case. As a consequence, we also obtain an explicit isomorphism from any semisimple Ariki--Koike algebra to the group…
We classify Enriques surfaces of zero entropy, or, equivalently, Enriques surfaces with a virtually abelian automorphism group.