Related papers: An Introduction to Counting Orbifolds
We develop a technique to study curves in a variety which has a degeneration into some union of varieties. The class of such varieties is very broad, but the theory becomes particularly useful when the variety has a degeneration into a…
We develop a non planar topological vertex formalism and we use it to study the A-model partition function $\mathcal{Z}_{top}$ of topological string on the class of toric Calabi-Yau threefolds (CY3) in large complex structure limit. To that…
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 compute all loop topological string amplitudes on orientifolds of local Calabi-Yau manifolds, by using geometric transitions involving SO/Sp Chern-Simons theory, localization on the moduli space of holomorphic maps with involution, and…
We introduce Orbifold Reduction, a new method for generating $2d$ $(0,2)$ gauge theories associated to D1-branes probing singular toric Calabi-Yau 4-folds starting from $4d$ $\mathcal{N}=1$ gauge theories on D3-branes probing toric…
Dimer models have been used in string theory to construct path algebras with relations that are 3-dimensional Calabi-Yau Algebras. These constructions result in algebras that share some specific properties: they are finitely generated…
We survey the foundations for Donaldson-Thomas invariants for stable sheaves on algebraic threefolds with trivial canonical bundle, with emphasis on the case of abelian threefolds.
We explain an experimental method to find CY-type differential equations of order $3$ related to modular functions of genus zero. We introduce a similar class of Calabi-Yau differential equations of order $5$, show several examples and make…
We study the curve counting invariants of Calabi--Yau 3-folds via the Weyl reflection along a ruled divisor. We obtain a new rationality result and functional equation for the generating functions of Pandharipande--Thomas invariants. When…
We compute the integral homology (including torsion), the topological K-theory, and the Hodge structure on cohomology of Calabi-Yau threefold hypersurfaces and complete intersections in Gorenstein toric Fano varieties. The methods are…
We develop some computational methods for the integrals over the 3-chains on the compact Calabi-Yau 3-folds that plays a prominent role in the analysis of the topological B-model in the context of the open mirror symmetry. We discuss such…
We present a complete classification of all arrangements of eight planes in projective threespace that give rise to double octic Calabi-Yau threefolds. Building on earlier work, we determine all 455 combinatorial types and describe the…
We propose a way to examine N=1 and N=2 string dualities on Calabi-Yau three-folds or extensions. Our way is to find out or to construct two types of toric representations of a Calabi-Yau three-fold, which contain phases topologically…
In this paper we generalize previous work on decomposition in three-dimensional orbifolds by 2-groups realized as analogues of central extensions, to orbifolds by more general 2-groups. We describe the computation of such orbifolds in…
We study type III contractions of Calabi-Yau threefolds containing a ruled surface over a smooth curve. We discuss the conditions necessary for the image threefold to by smoothable. We describe the change in Hodge numbers caused by this…
We study Calabi--Yau 3-folds with infinitely many divisorial contractions. We also suggest a method to describe Calabi--Yau 3-folds with the infinite automorphism group.
We define an integer-valued virtual count of embedded pseudo-holomorphic curves of two times a primitive homology class and arbitrary genus in symplectic Calabi--Yau $3$-folds, which can be viewed as an extension of Taubes' Gromov…
We study giant graviton expansions of the superconformal index of 4d orbifold/orientifold theories. In general, a giant graviton expansion is given as a multiple sum over wrapping numbers. It has been known that the expansion can be reduced…
We classify orbifolds obtained by taking the quotient of a three tori by abelian extensions of Z/n x Z/n automorphisms, where each torus has a multiplicative Z/n action (n=3,4 or 6). This 'completes' the classification of orbifolds of the…
These are lecture notes on non-K\"ahler complex threefolds presented at the MATRIX program ``The geometry of moduli spaces in string theory''. We review some basics of Calabi-Yau geometry in Section 1, describe topological features of the…