Yukinobu Toda 교수

The Donaldson-Thomas invariant is a curve counting invariant on Calabi-Yau 3-folds via ideal sheaves. Another counting invariant via stable pairs is introduced by Pandharipande and Thomas, which counts pairs of curves and divisors on them. These two theories are conjecturally equivalent via generating functions, called DT/PT correspondence. In this paper, we show the Euler characteristic version of DT/PT correspondence, using the notion of weak stability conditions and the wall-crossing formula.

In this paper, we describe the spaces of stability conditions on the triangulated categories associated to three dimensional crepant small resolutions. The resulting spaces have chamber structures such that each chamber corresponds to a birational model together with a special Fourier-Mukai transform. We observe that these spaces are covering spaces over certain open subsets of finite dimensional vector spaces and determine their deck transformations.

<!-- *** Custom HTML *** --> The notion of limit stability on Calabi–Yau 3-folds is introduced by the author to construct an approximation of Bridgeland–Douglas stability conditions at the large volume limit. It has also turned out that the wall-crossing phenomena of limit stable objects seem relevant to the rationality conjecture of the generating functions of Pandharipande–Thomas invariants. In this article, we shall make it clear how wallcrossing formula of the counting invariants of limit st

This note gives a generalization of spherical twists, and describe the autoequivalences associated to certain non-spherical objects. Typically these are obtained by deforming the structure sheaves of (0, -2)-curves on threefolds, or deforming P-objects introduced by D. Huybrechts and R. Thomas.

The goal of the present paper is to show the transformation formula of Donaldson–Thomas invariants on smooth projective Calabi–Yau 3-folds under birational transformations via categorical method. We also generalize the non-commutative Donaldson–Thomas invariants, introduced by B. Szendrői in a local (−1, −1)-curve example, to an arbitrary flopping contraction from a smooth projective Calabi–Yau 3-fold. The transformation formula between such invariants and the usual Donaldson–Thomas invariants a

The aim of this paper is twofold. First we give an explicit construction of the infinitesimal deformations of the category Coh(X) of coherent sheaves on a smooth projective variety X. Secondly, we show that any Fourier-Mukai transform :

We introduce the notion of Gepner type Bridgeland stability conditions on triangulated categories, which depends on a choice of an autoequivalence and a complex number. We conjecture the existence of Gepner type stability conditions on the triangulated categories of graded matrix factorizations of weighted homogeneous polynomials. Such a stability condition may give a natural stability condition for Landau-Ginzburg Bbranes, and correspond to the Gepner point of the stringy Khler moduli space of

We show that the moduli stacks of semistable sheaves on smooth projective varieties are analytic locally on their coarse moduli spaces described in terms of representations of the associated Ext–quivers with convergent relations. When the underlying variety is a Calabi–Yau [math] –fold, our result describes the above moduli stacks as critical loci analytic locally on the coarse moduli spaces. The results in this paper will be applied to the wall-crossing formula of Gopakumar–Vafa invariants defi

For a Calabi-Yau three-fold X, we explicitly compute the Donaldson-Thomas-type invariant counting pairs (F, V ), where F is a zero-dimensional coherent sheaf on X and V F is a twodimensional linear subspace, which satisfy a certain stability condition. This is a rank two version of the Donaldson-Thomas (DT)-invariant of rank one, studied by Li, Behrend-Fantechi and Levine-Pandharipande. We use the wall-crossing formula of DTinvariants established by Joyce-Song, Kontsevich-Soibelman.