Related papers: Hyperplane sections and stable derived categories
In this article, a new construction of derived equivalences is given. It relates different endomorphism rings and more generally cohomological endomorphism rings - including higher extensions - of objects in triangulated categories. These…
We apply a definition of generalised super Calabi-Yau variety (SCY) to supermanifolds of complex dimension one. One of our results is that there are two SCY's having reduced manifold equal to $\mathbb{P}^1$, namely the projective super…
The goal of the present paper is to calculate the complex structure moduli space K\"ahler potentials for hypersurfaces in weighted projective spaces and compare with the partition functions of their mirror GLSMs. We explicitly perform the…
Motivated by the Strominger-Yau-Zaslow conjecture, we study fibre spaces whose total space has trivial canonical bundle. Especially, we are interest in Calabi-Yau varieties with fibre structure. In this paper, we only consider semi-stable…
We review the ghost-free four-derivative terms for chiral superfields in $\mathcal{N}=1$ supersymmetry and supergravity. These terms induce cubic polynomial equations of motion for the chiral auxiliary fields and correct the scalar…
We show that the formal moduli space of a Calabi-Yau manifold $X^n$ carries a linear structure, as predicted by mirror symmetry. This linear structure is canonically associated to a splitting of the Hodge filtration on $H^n(X)$.
We discuss homological mirror symmetry of Fermat polynomials in terms of derived Morita equivalence between derived categories of coherent sheaves and Fukaya-Seidel categories (a.k.a. perfect derived categories of directed Fukaya…
We use Lagrangian torus fibrations on the mirror $X$ of a toric Calabi-Yau threefold $\check X$ to construct Lagrangian sections and various Lagrangian spheres on $X$. We then propose an explicit correspondence between the sections and line…
We prove homological mirror symmetry for projective hypersurfaces of sufficiently high degree using a functor from the wrapped Fukaya category of an affine hypersurface to the Fukaya category of its boundary at infinity.
We solved the long-standing problem of describing the cohomology ring of semiample hypersurfaces in complete simplicial toric varieties. Also, the monomial-divisor mirror map is generalized to a map between the whole Picard group and the…
Let $\X$ be a resolving subcategory of an abelian category. In this paper we investigate the singularity category $\ds(\underline\X)=\db(\mod\underline\X)/\kb(\proj(\mod\underline\X))$ of the stable category $\underline\X$ of $\X$. We…
Hypersurfaces of manifolds of constant nonzero sectional curvature are classificated according their restricted homogeneous holonomy groups.
In 1984, Charney and Lee defined a category of stable curves and exhibited a rational homology equivalence from its geometric realisation to (the analytification of) the moduli stack of stable curves, also known as the…
We prove homological mirror symmetry for the quintic Calabi-Yau 3-fold. The proof follows that for the quartic surface by Seidel (arXiv:math/0310414) closely, and uses a result of Sheridan (arXiv:1012.3238). In contrast to Sheridan's…
We give some simple examples of mirror Calabi-Yau fourfolds in Type II string theory. These are realised as toroidal orbifolds. Motivated by the Strominger, Yau, Zaslow argument we give explicitly the mirror transformation which maps Type…
Let $X$ be a compact connected Riemann surface of genus $g$, with $g\geq 2$, and ${\cal M}_{\xi}$ a smooth moduli space of fixed determinant semistable vector bundles of rank $n$, with $n\geq 2$, over $X$. Take a smooth anticanonical…
We explain how to relate the problem of finding a mirror manifold for a Calabi-Yau manifold to the problem of characterizing the rational homotopy types of closed K\"{a}hler manifolds.
We study the representation of a finite group acting on the cohomology of a non-degenerate, invariant hypersurface of a projective toric variety. We deduce an explicit description of the representation when the toric variety has at worst…
We consider Takahashi's categorical interpretation of the Berglund-Hubsch mirror symmetry conjecture for invertible polynomials in the case of chain polynomials. Our strategy is based on a stronger claim that the relevant categories satisfy…
We discuss what it means for a symmetric monoidal category to be a module over a commutative semiring category. Each of the categories of (1) cartesian monoidal categories, (2) semiadditive categories, and (3) connective spectra can be…