Related papers: Type I Vacua from Diagonal $Z_3$-Orbifolds
In this paper, motivated by a problem posed by Barry Mazur, we show that for smooth projective varieties over the rationals, the odd cohomology groups of degree less than or equal to the dimension can be modeled by the cohomology of an…
We investigate several models of coupled scalar fields that present discrete Z_2, Z_2 x Z_2, Z_3 and other symmetries. These models support topological domain wall solutions of the BPS and non-BPS type. The BPS solutions are stable, but the…
We prove that compact Calabi--Yau varieties with certain isolated singularities are projective. In dimension 3 we do this by analysis, supposing given conifold metrics. In higher dimensions it follows more readily from Ohsawa's degenerate…
We survey here the construction and the basic properties of descendent invariants in the theory of stable pairs on nonsingular projective 3-folds. The main topics covered are the rationality of the generating series, the functional…
The role of open strings is investigated in the context of AdS$_{3}$ flux vacua arising from type IIB orientifold reductions. On the one hand, contrary to expectations, the perturbative stability of certain recently found non-supersymmetric…
We classify discrete modular symmetries in the effective action of Type IIB string on toroidal orientifolds with three-form fluxes, emphasizing on $T^6/\mathbb{Z}_2$ and $T^6/(\mathbb{Z}_2\times \mathbb{Z}_2^\prime)$ orientifold…
We study the orbifold Gromov-Witten theory of the quotient C^3/Z_3 in all genera. Our first result is a proof of the holomorphic anomaly equations in the precise form predicted by B-model physics. Our second result is an exact crepant…
We study the complex deformations of orientifolds of D3-branes at toric CY singularities, using their description in terms of dimer diagrams. We describe orientifold quotients that have fixed lines or fixed points in the dimer, and…
We compute the dynamical degrees of certain compositions of reflections in points on a smooth cubic fourfold. Our interest in these computations stems from the irrationality problem for cubic fourfolds. Namely, we hope that they will…
In this paper we study the (equivariant) topological types of a class of 3-dimensional closed manifolds (i.e., 3-dimensional small covers), each of which admits a locally standard $(\mathbb{Z}_2)^3$-action such that its orbit space is a…
Motivated by physics, we propose two conjectures regarding the cohomology ring of the crepant resolutions of orbifolds and cohomological invariants of K-equivalent manifolds.
An invariant of three-dimensional orientable manifolds is built on the base of a solution of pentagon equation expressed in terms of metric characteristics of Euclidean tetrahedra.
We study spaces and moduli spaces of Riemannian metrics with non-negative Ricci or non-negative sectional curvature on closed and open manifolds. We construct, in particular, the first classes of manifolds for which these moduli spaces have…
We study special linear systems of surfaces of $\mathbb{P}^3$ interpolating nine points in general position having a quadric as fixed component. By performing degenerations in the blown-up space, we interpret the quadric obstruction in…
We investigate D-branes in orientifolds of WZW models. A connection between the conformal field theory approach to orientifolds and the target space motivated analysis is established. In particular, we associate previously constructed…
We construct a class of geometric twists of Calabi-Yau manifolds of Voisin-Borcea type (K3 x T^2)/Z_2 and study the superpotential in a type IIA orientifold based on this geometry. The twists modify the direct product by fibering the K3…
We compute a complete set of isomorphism classes of cubic fourfolds over $\mathbb{F}_2$. Using this, we are able to compile statistics about various invariants of cubic fourfolds, including their counts of points, lines, and planes; all…
We construct a large class of conformal interfaces between two-dimensional c=1 conformal field theories describing compact free bosons and their Z_2 orbifolds. The interfaces are obtained by constructing boundary states in the corresponding…
Compact Type IIB D=4, N=1 orientifolds have certain U(1) sigma model symmetries at the level of the effective Lagrangian. These symmetries are generically anomalous. We study the particular case of $Z_N$ orientifolds and find that these…
We discuss type IIB orientifolds with D-branes, and NSNS and RR field strength fluxes, with D-brane sectors leading to open string spectra with non-abelian gauge symmetry and charged chiral fermions. The closed string field strengths…