Related papers: Generalised Kummer constructions and Weil restrict…
In this study, we analyze gauge groups in six-dimensional $N=1$ F-theory models. We construct elliptic Calabi-Yau 3-folds possessing various singularity types as double covers of "1/2 Calabi-Yau 3-folds", a class of rational elliptic…
In this work we prove a bound for the torsion in Mordell-Weil groups of smooth elliptically fibered Calabi-Yau 3- and 4-folds. In particular, we show that the set which can occur on a smooth elliptic Calabi-Yau $n$-fold for ($n\geq 3$) is…
We establish optimal $(p,q)$ ranges for two types of estimates associated to three dimensional complex polynomial curves. These are the estimates for the weighted restriction of the Fourier Transform to a complex polynomial curve, and the…
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 construct Calabi-Yau 3-folds as orbifolds embedded in weighted projective space in codimension 4. For each Hilbert series that is realised, there are at least two different components of Calabi-Yau 3-folds.
We demonstrate a practical and efficient method for generating toric Calabi-Yau quiver theories, applicable to both D3 and M2 brane world-volume physics. A new analytic method is presented at low order parametres and an algorithm for the…
To a complex symplectic manifold X we associate a canonical quantization algebroid. Our construction is similar to that of Polesello-Schapira's deformation-quantization algebroid, but the deformation parameter is no longer central. If X is…
We construct Calabi-Yau threefolds defined over $\mathbb{Q}$ via quotients of abelian threefolds, and re-verify the rigid Calabi-Yau threefolds in this construction are modular by computing their L-series, without \cite{Dieulefait} or…
We construct the regularised Wheeler-De Witt operator demanding that the algebra of constraints of quantum gravity is anomaly free. We find that for a subset of all wavefunctions being integrals of scalar densities this condition can be…
Let f be a newform of weight at least 3 with Fourier coefficients in a number field K. We show that the universal deformation ring of the mod lambda Galois representation associated to f is unobstructed, and thus isomorphic to a power…
We propose two kinds of gauged linear sigma models whose moduli spaces are real eight-dimensional hyperKahler and Calabi-Yau manifolds, respectively. Here, hyperKahler manifolds have sp(2) holonomy in general and are dual to Type IIB…
Non-simply connected Calabi-Yau threefolds play a central role in the study of string compactifications. Such manifolds are usually described by quotienting a simply connected Calabi-Yau variety by a freely acting discrete symmetry. For the…
Calabi-Yau four-folds may be constructed as hypersurfaces in weighted projective spaces of complex dimension 5 defined via weight systems of 6 weights. In this work, neural networks were implemented to learn the Calabi-Yau Hodge numbers…
We analyze the structure of the set of limiting Carleman weights in all conformally flat manifolds, 3-manifolds, and 4-manifolds. In particular we give a new proof of the classification of Euclidean limiting Carleman weights, and show that…
In generalized complex geometry, we revisit linear subspaces and submanifolds that have an induced generalized complex structure. We give an expression of the induced structure that allows us to deduce a smoothness criteria, we dualize the…
We construct Bridgeland stability conditions on the the following hyper-K\"ahler or strict Calabi--Yau manifolds: - Generalized Kummer varieties associated to an abelian surface that is isogenous to a product of elliptic curves. - Universal…
We examine instances of modularity of (rigid) Calabi-Yau manifolds whose periods are expressed in terms of hypergeometric functions. The $p$-th coefficients $a(p)$ of the corresponding modular form can be often read off, at least…
We investigate Calabi--Yau three folds which are small resolutions of fiber products of elliptic surfaces with section admitting reduced fibers. We start by the classification of all fibers that can appear on such varieties. Then, we find…
We apply the Yau-Zaslow-Beauville method to compute the Euler characteristic of the generalized Kummer varieties attached to a complex abelian surface (a calculation also done by Goettsche and Soergel by different methods). It is related to…
We compute certain open Gromov-Witten invariants for toric Calabi-Yau threefolds. The proof relies on a relation for ordinary Gromov-Witten invariants for threefolds under certain birational transformation, and a recent result of Kwokwai…