Related papers: Stability Manifold of P^1
We investigate some aspects of Pi-stability of D-branes on Calabi-Yau threefolds in cases where there is a point in moduli space where the grades nearly or completely align. We prove that an example of complete alignment is the case of a…
In this paper, we introduce new enumerative invariants of curves on Calabi-Yau 3-folds via certain stable objects in the derived category of coherent sheaves. We introduce the notion of limit stability on the category of perverse coherent…
The notion that the geometry of spacetime is given by the moduli space of 0-branes is examined in four examples of Calabi-Yau threefolds. An important consideration when determining the moduli space of D-branes is the stability condition…
Homological stability for unordered configuration spaces of connected manifolds was discovered by Th. Church and extended by O. Randal-Williams and B. Knudsen: $H_i(C_k(M);\mathbb{Q})$ is constant for $k\geq f(i)$. We characterize the…
A triangulated category $\mathcal{C}$ with a canonical Bott's isomorphism $[2]\xrightarrow{\sim}id$ is called a cyclic category in this paper. We give a new notion of stability conditions on a $k$-linear Krull-Schmidt cyclic category. Given…
We establish a homotopy-theoretic description of the homology of stable moduli spaces of $(2n+1)$-dimensional manifold triads $(N, \partial^h N, \partial^v N)$ with fixed $\partial^v N$, whenever $n \geq 3$ and $(N, \partial^h N)$ is…
A set of necessary conditions for $C^1$ stability of noninvertible maps is presented. It is proved that the conditions are sufficient for $C^1$ stability in compact oriented manifolds of dimension two. An example given by F.Przytycki in…
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…
We describe a connected component of the space of stability conditions on abelian threefolds, and on Calabi-Yau threefolds obtained as (the crepant resolution of) a finite quotient of an abelian threefold. Our proof includes the following…
We develop a theory of Bridgeland stability conditions and moduli spaces of semistable objects for a family of varieties. Our approach is based on and generalizes previous work by Abramovich-Polishchuk, Kuznetsov, Lieblich, and…
In this short note, we provide a broad class of examples of stability conditions on the category of coherent sheaves which generalise Gieseker stability. We refer to them as "adapted to coherent sheaves" and they admit Harder--Narasimhan…
Identification of string junction states of pure SU(2) Seiberg-Witten theory as B-branes wrapped on a Calabi-Yau manifold in the geometric engineering limit is discussed. The wrapped branes are known to correspond to objects in the bounded…
We introduce two extensions of the space of Bridgeland stability conditions of a triangulated category. First we consider lax stability conditions where semistable objects are allowed to have mass zero but still have a phase. The…
A system containing a pair of non-BPS D-strings of type IIA string theory on an orbifold, representing a single D2-brane wrapped on a nonsupersymmetric 2-cycle of a Calabi-Yau 3-fold with $(h^{(1,1)},h^{(1,2)})$ = (11,11), is analyzed. In…
We give further counterexamples to the conjectural construction of Bridgeland stability on threefolds due to Bayer, Macr\`i, and Toda. This includes smooth projective threefolds containing a divisor that contracts to a point, and…
We consider a 3-Calabi-Yau triangulated category associated to an ideal triangulation of a marked bordered surface. Using the theory of harmonic maps between Riemann surfaces, we construct a natural map from a component of the space of…
We survey some aspects of stability conditions both in general and on the derived category of coherent sheaves on a surface, with applications to the birational geometry of certain holomorphic symplectic varieties.
The D-brane spectrum of a $\Zop_2\times\Zop_2$ Calabi-Yau three-fold orbifold of toroidally compactified Type IIA and Type IIB string theory is analysed systematically. The corresponding K-theory groups are determined and complete agreement…
We show that some Gieseker stable sheaves on a projective K3 surface $X$ are stable with respect to a stability condition of Bridgeland on the derived category of $X$ if the stability condition is in explicit subsets of the space of…
We study the space of stability conditions $\Stab(X)$ on the non-compact Calabi-Yau threefold $X$ which is the total space of the canonical bundle of $\PP^2$. We give a combinatorial description of an open subset of $\Stab(X)$ and state a…