Stratified local moduli of Calabi–Yau threefolds

Witten Geometric Quantization of the Moduli of CY Threefolds

In this paper we study two different topics. The first topic is the applications of the geometric quantization scheme of Witten introduced in [2] and [15] to the problem of the quantum background independence in string theory. The second topic is the introduction of a Z structure on the tangent space of the moduli space of polarized CY threefolds M(M). Based on the existence of a Z structure on...

Calabi-Yau Threefolds and Moduli of Abelian Surfaces I

Let Ad denote the moduli space of polarized abelian surfaces of type (1, d), and let A d be the moduli space of polarized abelian surfaces with canonical level structure. Both are (possibly singular) quasi-projective threefolds, and A d is a finite cover of Ad. We will also denote by Ãd and à d nonsingular models of suitable compactifications of these moduli spaces. We will use in the sequel de...

Asymptotic Curvature of Moduli Spaces for Calabi–yau Threefolds

Motivated by the classical statements of Mirror Symmetry, we study certain Kähler metrics on the complexified Kähler cone of a Calabi– Yau threefold, conjecturally corresponding to approximations to the Weil– Petersson metric near large complex structure limit for the mirror. In particular, the naturally defined Riemannian metric (defined via cup-product) on a level set of the Kähler cone is se...

Local positivity of principally polarized abelian threefolds

LOCAL BASES WITH STRATIFIED STRUCTURE IN $I$-TOPOLOGICAL VECTOR SPACES

In this paper, the concept of {sl local base with  stratifiedstructure} in $I$-topological vector spaces is introduced. Weprove that every $I$-topological vector space has a balanced localbase with stratified structure. Furthermore, a newcharacterization of $I$-topological vector spaces by means of thelocal base with stratified structure is given.