Isolated rational curves on K 3-fibered Calabi-Yau threefolds

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

In this paper we study 15 complete intersection K3-fibered Calabi–Yau variety types in biprojective space P1 × P These are all the CICY-types that are K3 fibered by the projection on the second factor. We prove existence of isolated rational curves of bidegree (d, 0) for every positive integer d on a general Calabi– Yau variety of these types. The proof depends heavily on existence theorems for...

Rational Curves on Calabi-yau Threefolds

In the conformal field theory arising from the compactification of strings on a Calabi-Yau threefold X, there naturally arise fields correspond to harmonic forms of types (2,1) and (1,1) on X [4]. The uncorrected Yukawa couplings in H and H are cubic forms that can be constructed by techniques of algebraic geometry — [20] contains a nice survey of this in a general context in a language written...

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...

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

Enumerating Curves in Calabi-yau Threefolds