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Yukinobu Toda

Publications and source records attributed to Yukinobu Toda.

80 records · Page 5Linked to original sources
arXiv2008

Birational Calabi-Yau 3-folds and BPS state counting

This paper contains some applications of Bridgeland-Douglas stability conditions on triangulated categories, and Joyce's work on counting invariants of semistable objects, to the study of birational geometry. We introduce the notion of motivic Gopakumar-Vafa invariants as counting invariants of D2-branes, and show that they are invariant under birational transformations between Calabi-Yau 3-folds. The result is similar to the fact that birational Calabi-Yau 3-folds have the same betti numbers or Hodge numbers.

math.AG↗
arXiv2007

Moduli stacks and invariants of semistable objects on K3 surfaces

For a K3 surface X and its bounded derived category of coherent sheaves D(X), we have the notion of stability conditions on D(X) in the sense of T.Bridgeland. In this paper, we show that the moduli stack of semistable objects in D(X) with a fixed numerical class and a phase is represented by an Artin stack of finite type over C. Then following D.Joyce's work, we introduce the invariants counting semistable objects in D(X), and show that the invariants are independent of a choice of a stability condition.

math.AG↗
arXiv2007

Fourier-Mukai transforms and canonical divisors

Let $X$ be a smooth projective variety. We study a relationship between the derived category of $X$ and that of a canonical divisor. As an application, we will study Fourier-Mukai transforms when $κ(X)=dim X-1$.

math.AG↗
arXiv2007

Deformations and Fourier-Mukai transforms

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 $/Phi/colon D^b(X)/to D^b(Y)$ extends to an equivalence between the derived categories of the deformed Abelian categories.

math.AG↗
arXiv2007

Stability conditions and crepant small resolutions

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 these spaces are covering spaces over certain open subsets of finite dimensional vector spaces, and determine their deck transformations.

math.AG↗
arXiv2006

Stability conditions and Calabi-Yau fibrations

In this paper, we describe the spaces of stability conditions for the triangulated categories associated to three dimensional Calabi-Yau fibrations. We deal with two cases, the flat elliptic fibrations and smooth K3 (Abelian) fibrations. In the first case, we will see there exist chamber structures similar to those of the movable cone used in birational geometry. In the second case, we will compare the space with the space of stability conditions for the closed fiber of the fibration.

math.AG↗
arXiv2006

On a certain generalization of spherical twists

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 $\mathbb{P}$-objects introduced by D.Huybrecht and R.Thomas

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