Related papers: $G_2$-Grassmannians and derived equivalences

We study the enumerative geometry of stable maps to Calabi-Yau 5-folds $Z$ with a group action preserving the Calabi-Yau form. In the central case $Z=X \times \mathbb{C}^2$, where $X$ is a Calabi-Yau 3-fold with a group action scaling the…

In this paper we study the relationship between three compactifications of the moduli space of Hermitian-Yang-Mills connections on a fixed Hermitian vector bundle over a projective algebraic manifold of arbitrary dimension. Via the…

Recently, at least 50 million of novel examples of compact $G_2$ holonomy manifolds have been constructed as twisted connected sums of asymptotically cylindrical Calabi-Yau threefolds. The purpose of this paper is to study mirror symmetry…

We prove that the generalized Grassmannian flops of both $D_4$ and $G_2^{\dagger}$ type induce derived equivalences, which provide new evidence for the DK conjecture by Bondal-Orlov and Kawamta. The proof is based on Kuznetsov's mutation…

This article studies the geometry of moduli spaces of G2-manifolds, associative cycles, coassociative cycles and deformed Donaldson-Thomas bundles. We introduce natural symmetric cubic tensors and differential forms on these moduli spaces.…

We introduce a homology theory whose Euler characteristics counts ASD bundles over four dimensional co-associative submanifolds in (almost) G_2 manifolds. As a TQFT, in relative situations, we have the Fukaya-Floer category of Lagrangians…

This note presents some properties of the variety of planes $F_2(X)\subset G(3,7)$ of a cubic $5$-fold $X\subset \mathbb P^6$. A cotangent bundle exact sequence is first derived from the remark made by Iliev and Manivel that $F_2(X)$ sits…

We present a new class of dualities relating non-geometric Calabi-Yau compactifications of type II string theory to T-fold compactifications of the heterotic string, both preserving four-dimensional $\mathcal{N}=2$ supersymmetry. The…

The two-dimensional supersymmetric gauged linear sigma model (GLSM) with abelian gauge groups and matter fields has provided many insights into string theory on Calabi--Yau manifolds of a certain type: complete intersections in toric…

We study the moduli space $\textsf{T}$ of the Calabi-Yau $n$-folds arising from the Dwork family and enhanced with bases of the $n$-th de Rham cohomology with constant cup product and compatible with Hodge filtration. We also describe a…

We give a differential-geometric construction of Calabi-Yau fourfolds by the `doubling' method, which was introduced in \cite{DY14} to construct Calabi-Yau threefolds. We also give examples of Calabi-Yau fourfolds from toric Fano fourfolds.…

Let $X$ denote the total space of cotangent bundle of projective plane. This is a non-compact Calabi-Yau $4$-fold (also called local Calabi-Yau variety in physics literature). The aim of this paper is to use tilting objects to characterize…

For a given Fourier-Mukai equivalence of bounded derived categories of coherent sheaves on smooth quasi-projective varieties, we construct Fourier-Mukai equivalences of derived factorization categories of gauged Landau-Ginzburg (LG) models.…

We define the notion of mirror of a Calabi-Yau manifold with a stable bundle in the context of type II strings in terms of supersymmetric cycles on the mirror. This allows us to relate the variation of Hodge structure for cohomologies…

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…

We analyse the possible ways of gluing twisted products of circles with asymptotically cylindrical Calabi-Yau manifolds to produce manifolds with holonomy G_2, thus generalising the twisted connected sum construction of Kovalev and Corti,…

We provide the complete classification of seven-dimensional manifolds endowed with a closed non-parallel G$_2$-structure and admitting a transitive reductive group G of automorphisms. In particular, we show that the center of G is…

We study one class of linear sigma models and their T-dualized theories for noncompact Calabi-Yau manifolds. In the low energy limit, we find that this system has various massless effective theories with orbifolding symmetries. This…

We construct new examples of non-formal simply connected compact Sasaki-Einstein 7-manifolds. We determine the minimal model of the total space of any fibre bundle over $CP^2$ with fibre $S^1\times S^2$ or $S^3/Z_p$ ($p>0$), and we apply…

We prove a general theorem that gives a non trivial relation in the group of derived autoequivalences of a variety (or stack) X, under the assumption that there exists a suitable functor from the derived category of another variety Y…