Related papers: A geometric application of Nori's connectivity the…

We show that Lang's hyperbolic and function version conjectures hold for surfaces $S$ of general type having a fibration of general type onto a curve $C$. The notion of multiplicity used is natural, but not classical, which leds to orbifold…

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…

In this paper we analyze the problem of uniqueness for spacelike hypersurfaces with constant higher order mean curvature in generalized Robertson-Walker spacetimes. We consider first the case of compact spacelike hypersurfaces, completing…

We show that any asymptotically Calabi manifold which is Calabi-Yau can be compactified complex analytically to a weak Fano manifold. Furthermore, the Calabi-Yau structure arises from a generalized Tian-Yau construction on the…

The connections amongst (1) quivers whose representation varieties are Calabi-Yau, (2) the combinatorics of bipartite graphs on Riemann surfaces, and (3) the geometry of mirror symmetry have engendered a rich subject at whose heart is the…

During the last years we have generated a large number of data related to Calabi-Yau hypersurfaces in toric varieties which can be described by reflexive polyhedra. We classified all reflexive polyhedra in three dimensions leading to K3…

Greene, Morrison and Plesser \cite{GMP} have recently suggested a general method for constructing a mirror map between a $d$-dimensional Calabi-Yau hypersurface and its mirror partner for $d > 3$. We apply their method to smooth…

We show that the (1,0) tensor and hypermultiplet supersymmetry variations can be uplifted to loop space. Upon dimensional reduction we make contact with abelian five-dimensional super Yang-Mills, which has a nonabelian generalization that…

In Calabi-Yau fourfold compactifications of M-theory with flux, we investigate the possibility of partial supersymmetry breaking in the three-dimensional effective theory. To this end, we place the effective theory in the framework of…

(1,d)-polarized abelian surfaces in P^(d-1) with two plane cubic curve fibrations lie in two elliptic P^2-scrolls. The union of these scrolls form a reducible Calabi-Yau 3-fold. In this paper we show that this occurs when d<10 and analyse…

We construct smooth Calabi-Yau threefolds Z, torus-fibered over a dP_9 base, with fundamental group Z_2 X Z_2. To do this, the structure of rational elliptic surfaces is studied and it is shown that a restricted subset of such surfaces…

A normal variety $X$ is called Calabi-Yau if $K_X \sim_{\mathbb Q} 0$. The index of $X$ is the smallest positive integer $m$ so that $m K_X \sim 0$. We construct smooth, projective Calabi-Yau varieties in every dimension with doubly…

In this article we introduce generalized projective spaces (Definitions $[2.1, 2.5]$) and prove three main theorems in two different contexts. In the first context we prove, in main Theorem $A$, the surjectivity of the Chinese remainder…

We start a systematic study of non-projected supermanifolds, concentrating on supermanifolds with fermionic dimension 2 and with the reduced manifold a complex projective space. We show that all the non-projected supermanifolds of dimension…

By a theorem of Wahl, the canonically embedded curves which are hyperplane section of K3 surfaces are distinguished by the non-surjectivity of their Wahl map. In this paper we address the problem of distinguishing hyperplane sections of…

We study a natural generalization of transversally intersecting smooth hypersurfaces in a complex manifold: hypersurfaces, whose components intersect in a transversal way but may be themselves singular. Such hypersurfaces will be called…

In this paper, we establish a structure theorem for projective klt pairs $(X,\Delta)$ with nef anti-log canonical divisor; specifically, we prove that, up to replacing $X$ with a finite quasi-\'etale cover, $X$ admits a locally trivial…

We show that the class of twisted fractionally Calabi-Yau algebras of finite global dimension coincides with the stable endomorphism algebras of $d$-cluster tilting modules over $d$-representation-finite algebras. This is an application of…

We apply a universal normal Calabi-Yau algebra to the construction and classification of compact complex $n$-dimensional spaces with SU(n) holonomy and their fibrations. This algebraic approach includes natural extensions of reflexive…

I construct some smooth Calabi-Yau threefolds in characteristic two and three that do not lift to characteristic zero. These threefolds are pencils of supersingular K3-surfaces. The construction depends on Moret-Bailly's pencil of abelian…