Isolated Rational Curves on K 3 - Fibered Calabi – Yau Threefolds

Arithmetic and Geometry of Algebraic Varieties with Special Emphasis on Calabi–yau Varieties and Mirror Symmetry

Chen, Xi (University of Alberta) Xiao’s Conjecture on Canonically Fibered Surfaces Abstract: In 1988, Gang Xiao proposed a list of open problems on algebraic surfaces. Many of these remain open to this day. One of the problems concerns the maximal relative genus of a canonically fibered surface. In this talk, I will talk about my proof of this conjecture. Garcia, Natalia (Queen’s University) Cu...

1 4 A pr 1 99 9 K 3 - fibered Calabi - Yau threefolds II , singular fibers

Constructing Balanced Metrics on Some Families of Non-kähler Calabi-yau Threefolds

We construct balanced metrics on the family of non-Kähler CalabiYau threefolds that are obtained by smoothing after contracting (−1,−1)-rational curves on Kähler Calabi-Yau threefold. As an application, we construct balanced metrics on complex manifolds diffeomorphic to connected sum of k ≥ 2 copies of S × S.

On Isolated Smooth Curves of Low Genera in Calabi-yau Complete Intersection Threefolds

Building on results of Clemens and Kley, we find criteria for a continuous family of curves in a nodal K-trivial threefold Y0 to deform to a scheme of finitely many smooth isolated curves in a general deformation Yt of Y0. As an application, we show the existence of smooth isolated curves of bounded genera and unbounded degrees in Calabi-Yau complete intersection threefolds.

On the Hodge structure of elliptically fibered Calabi-Yau threefolds

The Hodge numbers of generic elliptically fibered Calabi-Yau threefolds over toric base surfaces fill out the “shield” structure previously identified by Kreuzer and Skarke. The connectivity structure of these spaces and bounds on the Hodge numbers are illuminated by considerations from F-theory and the minimal model program. In particular, there is a rigorous bound on the Hodge number h21 ≤ 49...