Related papers: Intersections of two Grassmannians in $\mathbf{P}^…
In this paper we compute genus 0 orbifold Gromov--Witten invariants of Calabi--Yau threefold complete intersections in weighted projective stacks, regardless of convexity conditions. The traditional quantumn Lefschetz principle may fail…
A noncommutative Grassmannian NGr(m, n) is introduced by Efimov, Luntz, and Orlov in `Deformation theory of objects in homotopy and derived categories III: Abelian categories' as a noncommutative algebra associated to an exceptional…
We study the local geometry of the moduli space of intermediate Jacobians of $(2,2)$-threefolds in ${\mathbb P}^2 \times {\mathbb P}^2$. More precisely, we prove that a composition of the second fundamental form of the Siegel metric in…
We exhibit isomorphisms of Grassmann spaces and their relationship with collineations and embeddings of the underlying projective spaces.
In this paper we outline some aspects of nonabelian gauged linear sigma models. First, we review how partial flag manifolds (generalizing Grassmannians) are described physically by nonabelian gauged linear sigma models, paying attention to…
We give two new examples of families of Calabi-Yau complete intersection threefolds whose generic element contains infinitely many lines. We get some results about the normal bundles of these lines and the Hilbert scheme of lines on the…
In previous work, it was argued that the type IIB T^6/Z_2 orientifold with a choice of flux preserving N=2 supersymmetry is dual to a class of purely geometric type IIA compactifications on abelian surface (T^4) fibered Calabi-Yau…
We develop some methods to construct normal crossing varieties whose dual complexes are two-dimensional, which are smoothable to Calabi--Yau threefolds. We calculate topological invariants of smoothed Calabi--Yau threefolds and show that…
We present solutions for the higher genus topological string amplitudes on Calabi-Yau-manifolds, which are realized as complete intersections in Grassmannians. We solve the B-model by direct integration of the holomorphic anomaly equations…
We investigate a potential relationship between mirror symmetry for Calabi-Yau manifolds and the mirror duality between quasi-Fano varieties and Landau-Ginzburg models. More precisely, we show that if a Calabi-Yau admits a so-called Tyurin…
We describe deformations of the noncompact Calabi-Yau threefolds $W_k = \mbox{Tot}(\mathcal{O}_{\mathbb{P}^1}(-k) \oplus \mathcal{O}_{\mathbb{P}^1}(k-2))$ for $k=1,2,3$, as well as their moduli of holomorphic vector bundles of rank $2$.…
In this work we study the phase structure of skew symplectic sigma models, which are a certain class of two-dimensional N = (2,2) non-Abelian gauged linear sigma models. At low energies some of them flow to non-linear sigma models with…
The aim of this article is to report on recent progress in understanding mirror symmetry for some non-complete intersection Calabi-Yau threefolds. We first construct four new smooth non-complete intersection Calabi-Yau threefolds with…
A homogeneous roof is a rational homogeneous variety of Picard rank 2 and index $r$ equipped with two different $\mathbb P^{r-1}$-bundle structures. We consider bundles of homogeneous roofs over a smooth projective variety, formulating a…
We prove a sort of reconstruction theorem for generic elliptic Calabi-Yau $3$-folds in the sense of C\u{a}ld\u{a}raru. From our argument it follows that two generic elliptic Calabi-Yau $3$-folds are derived-equivalent linear over the base…
We shall give an explicit pair of birational projective Calabi--Yau threefolds which are rigid, non-homeomorphic, but are connected by projective flat deformation over some connected base scheme.
In this article, we study the geometry of log Calabi-Yau pairs $(X,B)$ of index one and birational complexity zero. Firstly, we propose a conjecture that characterizes such pairs $(X,B)$ in terms of their dual complex and the rationality of…
Previously we constructed Calabi-Yau threefolds by a differential-geometric gluing method using Fano threefolds with their smooth anticanonical $K3$ divisors (New York J. Math. 20: 1-33, 2014). In this paper, we further consider the…
In order to support the odd moduli in models of (type IIB) string compactification, we classify the Calabi-Yau threefolds with h^{1,1}<=4 which exhibit pairs of identical divisors, with different line-bundle charges, mapping to each other…
We discuss a conjecture saying that derived equivalence of simply connected smooth projective varieties implies that the difference of their classes in the Grothendieck ring of varieties is annihilated by a power of the affine line class.…