Related papers: Exceptional sequences of maximal length on some su…

We construct exceptional sequences of line bundles of maximal length on a family of surfaces isogenous to a higher product of unmixed type with $p_g=q=0$.

We construct exceptional collections of line bundles of maximal length 4 on $S=(C \times D)/G$ which is a surface isogenous to a higher product with $p_g=q=0$ where $G=G(32,27)$ is a finite group of order 32 having number 27 in the list of…

We construct exceptional collections of maximal length on four families of surfaces of general type with $p_g=q=0$ which are isogenous to a product of curves. From these constructions we obtain new examples of quasiphantom categories as…

We use constructions of surfaces as abelian covers to write down exceptional collections of line bundles of maximal length for every surface $X$ in certain families of surfaces of general type with $p_g=0$ and $K_X^2=3,4,5,6,8$. We also…

We provide an explicit description of exceptional collection of maximal length in the derived category $D^b(Y)$ for a particular class of elliptic surfaces $Y$. The existence of non\,-\,trivial semiorthogonal complement (a "\,phantom\,") of…

We construct an infinite family of homologous, non-isotopic, symplectic surfaces of any genus greater than one in a certain class of closed, simply connected, symplectic four-manifolds. Our construction is the first example of this…

We construct an exceptional sequence of length 11 on the classical Godeaux surface X which is the Z/5-quotient of the Fermat quintic surface in P^3. This is the maximal possible length of such a sequence on this surface which has…

For a smooth projective toric variety of Picard rank two we classify all exceptional sequences of invertible sheaves which have maximal length. In particular, we prove that unlike non-maximal sequences, they (a) remain exceptional under…

We investigate combinatorial aspects of exceptional sequences in the derived category of coherent sheaves on certain smooth and complete algebraic surfaces. We show that to any such sequence there is canonically associated a complete toric…

We prove that the bounded derived category of the surface S constructed by Barlow admits a length 11 exceptional sequence consisting of (explicit) line bundles. Moreover, we show that in a small neighbourhood of S in the moduli space of…

Regular algebraic surfaces isogenous to a higher product of curves can be obtained from finite groups with ramification structures. We find unmixed ramification structures for finite groups constructed as p-quotients of particular infinite…

Inspired by Bondal's conjecture, we study the behavior of exceptional sequences of line bundles on rational C*-surfaces under homogeneous degenerations. In particular, we provide a sufficient criterion for such a sequence to remain…

We generalise a method of Xiao Gang to construct 'prototypes' of fibred surfaces with maximal irregularity without being a product. This enables us, in the case of fibre genus g=3 to describe the possible singular fibres and to calculate…

We restrict our discussion to the orientable category. For $g > 1$, let $OE_g$ be the maximum order of a finite group $G$ acting on the closed surface $\Sigma_g$ of genus $g$ which extends over $(S^3, \Sigma_g)$, where the maximum is taken…

We construct some complex surfaces of general type with maximal Picard number. These examples arise as fibrations of genus two curves over quaternionic Shimura curves.

We find all exceptional spin groups attached to the vertices of any exceptional spin graph on any hyperbolic Riemann surface S of genus g>1. In particular, we show that when the order r of a graph is r>2 (i.e.the genus of S must be g>3)…

We investigate maximal exceptional sequences of line bundles on (P^1)^3, i.e. those consisting of 2^r elements. For r=3 we show that they are always full, meaning that they generate the derived category. Everything is done in the discrete…

Let $G$ be a finite group. By a sequence over $G$, we mean a finite unordered sequence of terms from $G$, where repetition is allowed, and we say that it is a product-one sequence if its terms can be ordered such that their product equals…

We consider a surface that admits a $\mathbb{Q}$-Gorenstein degeneration to a cyclic quotient singularity $\frac{1}{dn^2}(1,dna-1)$. Under several technical assumptions, we construct $d$ exceptional vector bundles of rank $n$ which are…

We construct an exceptional collection $\Upsilon$ of maximal possible length 6 on any of the Burniat surfaces with $K_X^2=6$, a 4-dimensional family of surfaces of general type with $p_g=q=0$. We also calculate the DG algebra of…