In this paper,we study the Shafarevich conjecture for moduli space of polarized Calabi-Yau manifolds and obtain some results on the rigidity of families of Calabi-Yau manifolds. We use variation of Hodge structure and Higgs bundle to establish a criterion for rigidity and apply it to show some important families of Calabi-Yau manifolds are rigid,for examples: Lefschetz pencils of Calabi-Yau man...

1Department of Psychiatry, National Cheng Kung University Hospital, College of Medicine, National Cheng Kung University, Tainan, Taiwan 2Institute of Behavioral Medicine, National Cheng Kung University Hospital, College of Medicine, National Cheng Kung University, Tainan, Taiwan 3Institute of Allied Health Sciences, College of Medicine and Hospital, National Cheng Kung University, Tainan, Taiwa...

We study, as hypersurfaces in toric varieties, elliptic Calabi–Yau fourfolds for F-theory compactifications dual to E8 × E8 heterotic strings compactified to four dimensions on elliptic Calabi–Yau threefolds with some choice of vector bundle. We describe how to read off the vector bundle data for the heterotic compactification from the toric data of the fourfold. This map allows us to construct...

The Calabi-Yau property of cocommutative Hopf algebras is discussed by using the homological integral, a recently introduced tool for studying infinite dimensional AS-Gorenstein Hopf algebras. It is shown that the skew-group algebra of a universal enveloping algebra of a finite dimensional Lie algebra g with a finite subgroup G of automorphisms of g is Calabi-Yau if and only if the universal en...

This note considers feedback stabilization of discrete-time linear time-varying systems. An operator-theoretic formulation of time-varying systems is used which allows the development to follow closely the linear time-invariant case. Using this framework, an extended Lyapunov stability result is derived. This leads to a direct proof of a feedback stabilization scheme due to Cheng without the us...

We consider two-dimensional supergravity theories with four supercharges constructed from compactification of Type II string theory on a generic Calabi-Yau four-fold. In Type IIA and Type IIB cases, respectively, new superspace formulations of N = (2, 2) and N = (0, 4) dilaton supergravities are found and their coupling to matter multiplets is discussed. 1. Introduction For a long time, compact...

The Rarita-Schwinger operator is the twisted Dirac restricted to 3/2-spinors. fields are solutions of this which in addition divergence-free. This an overdetermined problem and rare; it even more unexpected for there be large dimensional spaces solutions. In paper we prove existence a sequence compact manifolds any given dimension greater than or equal 4 space tends infinity. These either simpl...

Gromov-Witten theory is used to define an enumerative geometry of curves in Calabi-Yau 4-folds. The main technique is to find exact solutions to moving multiple cover integrals. The resulting invariants are analogous to the BPS counts of Gopakumar and Vafa for Calabi-Yau 3-folds. We conjecture the 4-fold invariants to be integers and expect a sheaf theoretic explanation. Several local Calabi-Ya...

We consider smooth complete intersection Calabi–Yau 3-folds in minuscule Schubert varieties, and study their mirror symmetry by degenerating the ambient Schubert varieties to Hibi toric varieties. We list all possible Calabi–Yau 3-folds of this type up to deformation equivalences, and find a new example of smooth Calabi–Yau 3-folds of Picard number one; a complete intersection in a locally fact...