Related papers: Attractors are not algebraic
We study attractor points for Calabi-Yau variations of Hodge structures. In particular, for certain moduli spaces which are Shimura varieties, we prove that the attractor points are CM points, thus proving Moore's Attractor Conjecture in…
The moduli stacks of Calabi-Yau varieties are known to enjoy several hyperbolicity properties. The best results have so far been proven using sophisticated analytic tools such as complex Hodge theory. Although the situation is very…
We show how Moore's observation, in the context of toroidal compactifications in type IIB string theory, concerning the complex multiplication structure of black hole attractor varieties, can be generalized to Calabi-Yau compactifications…
Black holes in string theory compactified on Calabi-Yau varieties a priori might be expected to have moduli dependent features. For example the entropy of the black hole might be expected to depend on the complex structure of the manifold.…
We discuss the Hodge theory of algebraic non-commutative spaces and analyze how this theory interacts with the Calabi-Yau condition and with mirror symmetry. We develop an abstract theory of non-commutative Hodge structures, investigate…
We study black hole attractor equations for one-(complex structure)modulus Calabi-Yau spaces which are the mirror dual of Fermat Calabi-Yau threefolds (CY_{3}s). When exploring non-degenerate solutions near the Landau-Ginzburg point of the…
We prove that the irreducible components of the moduli space of polarized Calabi-Yau pairs are projective.
We investigate the complex and K\"ahler attractor mechanisms of moduli spaces of Calabi-Yau 3-folds. The complex attractor mechanism was previously studied by Ferrara-Kallosh-Strominger, Moore and others in string theory. It is concerned…
In this paper, we will study the arithmetic geometry of rank-2 attractors, which are Calabi-Yau threefolds whose Hodge structures admit interesting splits. We will develop methods to analyze the algebraic de Rham cohomologies of rank-2…
We prove that the 4-dimensional Galois representations associated with a certain Calabi-Yau threefold are reducible, with 2-dimensional composition factors coming from specific modular forms of weights 2 and 4, both level 14. This was…
In this paper we propose two guiding principles that suggest a number of conjectures (some now proved) about various forms of rigidity for moduli spaces arising in algebraic geometry. Such conjectures have group-theoretic, topological and…
Over any field of positive characteristic we construct 2-CY-tilted algebras that are not Jacobian algebras of quivers with potentials. As a remedy, we propose an extension of the notion of a potential, called hyperpotential, that allows to…
We consider attractor varieties arising in the construction of dyonic black holes in Calabi-Yau compactifications of IIB string theory. We show that the attractor varieties are constructed from products of elliptic curves with complex…
We formulate a version of the integral Hodge conjecture for categories, prove the conjecture for two-dimensional Calabi-Yau categories which are suitably deformation equivalent to the derived category of a K3 or abelian surface, and use…
Attractors of cooperative dynamical systems are particularly simple; for example, a nontrivial periodic orbit cannot be an attractor. This paper provides characterizations of attractors for the wider class of coherent systems, defined by…
The goal is to verify the Hodge conjecture (and some related conjectures) for certain moduli spaces. It is shown that the (generalized) Hodge conjecture holds for the projective moduli spaces of vector bundles over an abelian or K3 surface…
We prove that indecomposable transjective modules over cluster-tilted algebras are uniquely determined by their dimension vectors. Similarly, we prove that for cluster-concealed algebras, rigid modules lifting to rigid objects in the…
In the acyclic case, we establish a one-to-one correspondence between the tilting objects of the cluster category and the clusters of the associated cluster algebra. This correspondence enables us to solve conjectures on cluster algebras.…
In two recent papers, we described some Siegel modular threefolds which admit a weak Calabi--Yau model. Not all of them admit a {\it projective} model. The purpose of this paper is to exhibit criterions for the projectivity, to treat…
We show that special perturbations of a particular holomorphic map on $\mathbf{P}^k$ give us examples of maps that possess chaotic nonalgebraic attractors. Furthermore, we study the dynamics of the maps on the attractors. In particular, we…