Related papers: Exoflops in Two Dimensions
We study the Dirichlet energy of some smooth maps appearing in a collapsing family of hyper-K\"ahler metrics on the $K3$ surface constructed by Foscolo. We introduce an invariant for homotopy classes of smooth maps from the $K3$ surface…
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…
In this note, we prove that any non-collapsing and compact Gromov-Hausdorff limit of Kahler-Einstein manifolds is either smooth or is orbifold outside a subvariety of complex codimension at least 3.
We show that a Hilbert scheme of conics on a Fano fourfold double cover of $\mathbb{P}^2\times\mathbb{P}^2$ ramified along a divisor of bidegree $(2,2)$ admits a $\mathbb{P}^1$-fibration with base being a hyper-K\"{a}hler fourfold. We…
An extrinsic curvature surface model is investigated by Monte Carlo simulations on a disk. We found that the model undergoes a first-order transition separating the smooth phase from the collapsed phase. The results in this paper together…
We study topological properties of the D-brane resolution of three-dimensional orbifold singularities, C^3/Gamma, for finite abelian groups Gamma. The D-brane vacuum moduli space is shown to fill out the background spacetime with…
We study the surface behavior of the two-dimensional columnar dimerized quantum antiferromagnetic XXZ model with easy-plane anisotropy, with particular emphasis on the surface critical behaviors of the (2+1)-dimensional quantum critical…
In a holomorphic family $(X_b)_{b\in B}$ of non-K\"ahlerian compact manifolds, the holomorphic curves representing a fixed 2-homology class do not form a proper family in general. The deep source of this fundamental difficulty in…
A fundamental result in 4-manifold topology asserts that any two exotic smooth structures on a simply-connected, closed 4-manifold differ by a cork twist: the operation of removing a compact, contractible, codimension-zero submanifold and…
We study when the derived intersection of two smooth subvarieties of a smooth variety is formal. As a consequence we obtain a derived base change theorem for non-transversal intersections. We also obtain applications to the study of the…
We prove some results on the fibers and images of rational maps from a hyper-K\"ahler manifold. We study in particular the minimal genus of fibers of a fibration into curves. The last section of this paper is devoted to the study of the…
We define a signed count of real rational pseudo-holomorphic curves appearing in a one-parameter family of real Spin symplectic K3 surfaces. We show that this count is an invariant of the deformation class of the family. In the case of a…
We find upper bounds, sharp in most cases, on the number of real hyperplane sections of real smooth polarized $K3$-surfaces that split into lines. Most bounds coincide with their complex counterparts.
We obtain actions for N D-branes occupying points in a manifold with arbitrary Kahler metric. In one complex dimension, the action is uniquely determined (up to second order in commutators) by the requirement that it reproduce the masses of…
Computer simulations and scaling theory are used to investigate the damping of oscillations during epitaxial growth on high-symmetry surfaces. The crossover from smooth to rough growth takes place after the deposition of (D/F)^\delta…
Let M be a 2n-dimensional smooth and compact moduli space of stable sheaves on a K3 surface S and U a universal sheaf over S x M. Over M x M there exists a natural reflexive sheaf E of rank 2n-2, namely the first relative extension sheaf of…
The type IIB supergravity solution describing a collection of regular and fractional D3 branes on the conifold (hep-th/0002159) was recently generalized to the case of the deformed conifold (hep-th/0007191). Here we present another…
We study the existence of geometrically controlled branched covering maps from $\mathbb R^3$ to open $3$-manifolds or to decomposition spaces $\mathbb S^3/G$, and from $\mathbb S^3/G$ to $\mathbb S^3$.
We discuss local F-theory geometries and theirs gauge theory dualities in terms of intersecting D7-branes wrapped four-cycles in Type IIB superstring. The manifolds are built as elliptic K3 surface fibrations over intersecting F_0=CP^1…
We construct a collection of higher Chow cycles on certain surfaces which degenerate to an arrangement of planes in general position. When its degree is 4, this construction gives a new explicit proof of the Hodge-D-Conjecture for a certain…