Related papers: Autoequivalences of toric surfaces
This paper studies the class of spherical objects over any Kodaira $n$-cycle of projective lines and provides a parametrization of their isomorphism classes in terms of closed curves on the $n$-punctured torus without self-intersections.…
This is a systematic exposition of recent results which completely describe the group of automorphisms and the group of autoequivalences of generic analytic K3 surfaces. These groups, hard to determine in the algebraic case, admit a good…
We introduce a new class of autoequivalences that act on the derived categories of certain vector bundles over Grassmannians. These autoequivalences arise from Grassmannian flops: they generalize Seidel-Thomas spherical twists, which can be…
We survey some recent results concerning the so called Categorical Torelli problem. This is to say how one can reconstruct a smooth projective variety up to isomorphism, by using the homological properties of special admissible…
In this paper, we prove that each automorphism of the Torelli group of a surface is induced by a diffeomorphism of the surface, provided that the surface is a closed, connected, orientable surface of genus at least 3. This result was…
We investigate the bounded derived category of coherent sheaves on irreducible singular projective curves of arithmetic genus one. A description of the group of exact auto-equivalences and the set of all t-structures of this category is…
We present a construction of autoequivalences of derived categories of symmetric algebras based on projective modules with periodic endomorphism algebras. This construction generalises autoequivalences previously constructed by…
We prove that two derived equivalent twisted K3 surfaces have isomorphic periods. The converse is shown for K3 surfaces with large Picard number. It is also shown that all possible twisted derived equivalences between arbitrary twisted K3…
Given two semistable, non potentially isotrivial elliptic surfaces over a curve $C$ defined over a field of characteristic zero or finitely generated over its prime field, we show that any compatible family of effective isometries of the…
In this note, we show that there exists an autoequivalence of positive categorical entropy on the derived category of bielliptic surfaces. This gives the first example of a surface admitting positive categorical entropy in the absence of…
We explicitly describe the derived Picard groups of symmetric representation-finite algebras of type $D$. In particular, we prove that these groups are generated by spherical twists along collections of $0$-spherical objects, the shift and…
It was proved by Tien-Cuong Dinh and me that there is a smooth complex projective surface whose automorphism group is discrete and not finitely generated. In this paper, we will show that there is a smooth projective surface, birational to…
For each closed orientable surface we introduce a simplical complex with some additional structure which is a version of the complex of curves of this surface adjusted to investigation of its Torelli group. We call this complex the Torelli…
Derived equivalences of twisted K3 surfaces induce twisted Hodge isometries between them; that is, isomorphisms of their cohomologies which respect certain natural lattice structures and Hodge structures. We prove a criterion for when a…
We classify all smooth projective toric surfaces $S$ containing exactly one exceptional curve. We show that every such surface $S$ is isomorphic to either $\mathbb{F}_1$ or a surface $S_r$ defined by a rational number $r \in \mathbb{Q}…
Our main result is the determination of the respective groups $ Aut_\mathbb{Z}(S) $ of cohomologically trivial automorphisms and $ Aut_\mathbb{Q}(S) $ of numerically trivial automorphisms for the reducible fake quadrics, that is, the…
We provide a new and very short proof of the fact that a spherical functor between certain triangulated categories induces an autoequivalence.
Let a and b be two simple closed curves on an orientable surface S such that their geometric intersection number is greater than 1. It is known that the group generated by corresponding Dehn twists t_a and t_b is isomorphic to the free…
We determine some of the derived equivalences of a class of gentle algebras called surface algebras. These algebras are constructed from an unpunctured Riemann surface of genus 0 with boundary and marked points by introducing cuts in…
We construct new examples of derived autoequivalences for a family of higher-dimensional Calabi-Yau varieties. Specifically, we take the total spaces of certain natural vector bundles over Grassmannians G(r,d) of r-planes in a d-dimensional…