arXiv subjects
Publications and source records attributed to Kota Yoshioka.
We shall study birational maps of moduli spaces of stable sheaves on a K3 surface with Picard number 1 induced by Fourier-Mukai transforms.
For a Fourier-Mukai transform whose kernel is a family of Gieseker stable sheaves, we shall give a condition for the preservation of Gieseker stability of sheaves.
For a Fourier-Mukai transform whose kernel is the Poincare line bundle, we study the preservation of Gieseker stability of sheaves on any abelian surface. As an application, we give remarks on the weak Brill-Noether property.
We shall introduce a stability condition for a coherent sheaf associated to an elliptic surface. Then we study the behavior under relative Fourier-Mukai transforms.
We study the non-emptyness of moduli of stable sheaves on an elliptic ruled surface with a nef. anticanonical bundle.
We study the cohomology of a general stable sheaf on an abelian surface. We say that a moduli space satisfies weak Brill-Noether if the general sheaf has at most one non-zero cohomology group. Let $(X,H)$ be a polarized abelian surface and let $\mathbf{v}=(r,ξ,a)$ be a Mukai vector on $X$ with $\mathbf{v}^2\ge 0$,$r>0$, and $ξ\cdot H>0$. We show that if $ρ(X)=1$ or $ρ(X)=2$ and $X$ contains an elliptic curve, then all the moduli spaces $M_{X,H}(\mathbf{v})$ satisfy weak Brill-Noether. Conversely, if $ρ(X)>2$ or $ρ(X)=2$ and $X$ does not contain an elliptic curve, we show that there are infinitely many moduli spaces $M_{X,H}(\mathbf{v})$ that fail weak Brill-Noether. As a consequence, we classify Chern classes of Ulrich bundles on abelian surfaces.
We shall study stability conditions and Fourier-Mukai transforms on an elliptic surface. In particular we shall explain duality of elliptic surfaces by Fourier-Mukai transforms.
We shall study the wall crossing behavior of moduli of stable sheaves on an elliptic surface.
We shall study moduli spaces of stable 1-dimensional sheaves on an elliptic ruled surface.
We provide a criterion for when Hilbert schemes of points on K3 surfaces are birational. In particular, this allows us to generate a plethora of examples of non-birational Hilbert schemes which are derived equivalent.
In this note, we shall compute the categorical entropy of an autoequivalence on a generic abelian surface.
We give some remarks on our papers with Minamide and Yanagida on Bridgeland stability conditions. We also give a remark on stability conditions on Enriques surfaces, and give another proof of the projectivity of the coarse moduli spaces of semi-stable objects, which were obtained by Nuer.
We shall study a necessary and sufficient condition for the existence of stable sheaves on arbitrary Enriques surfaces.
We shall study the existence condition of slope stable sheaves on Enriques surfaces. We also gives a different proof of the irreducibility of the moduli spaces of rank 2 stable sheaves.
We give a different proof of Nuer's result on the exsistence of stable sheaves on Enriques surfaces.
We give a remark on the wall crossing behavior of perverse coherent sheaves on a blow-up and stability condition constructed by Toda. We also explain the wall crossing of twisted stability in terms of stability condition.
We shall study the chamber structure of positive cone of the albanese fiber of the moduli spaces of stable objects on an abelian surfaces via the chamber structure of stability conditions.
In the prequel to this paper, two versions of Le Potier's strange duality conjecture for sheaves over abelian surfaces were studied. A third version is considered here. In the current setup, the isomorphism involves moduli spaces of sheaves with fixed determinant and fixed determinant of the Fourier-Mukai transform on one side, and moduli spaces where both determinants vary, on the other side. We first establish the isomorphism in rank one using the representation theory of Heisenberg groups. For product abelian surfaces, the isomorphism is then shown to hold for sheaves with fiber degree 1 via Fourier-Mukai techniques. By degeneration to product geometries, the duality is obtained generically for a large number of numerical types. Finally, it is shown in great generality that the Verlinde sheaves encoding the variation of the spaces of theta functions are locally free over moduli.