On the Hodge structure of elliptically fibered Calabi-Yau threefolds
نویسنده
چکیده
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 ≤ 491 for any elliptically fibered Calabi-Yau threefold. The threefolds with the largest known Hodge numbers are associated with a sequence of blow-ups of toric bases beginning with the Hirzebruch surface F12 and ending with the toric base for the F-theory model with largest known gauge group.
منابع مشابه
6D F-theory models and elliptically fibered Calabi-Yau threefolds over semi-toric base surfaces
We carry out a systematic study of a class of 6D F-theory models and associated Calabi-Yau threefolds that are constructed using base surfaces with a generalization of toric structure. In particular, we determine all smooth surfaces with a structure invariant under a single C∗ action (sometimes called “T-varieties” in the mathematical literature) that can act as bases for an elliptic fibration ...
متن کاملF-theory Duals of M-theory on G2 Manifolds from Mirror Symmetry
Using mirror pairs (M3,W3) in type II superstring compactifications on Calabi-Yau threefols, we study, geometrically, F-theory duals of M-theory on seven manifolds with G2 holonomy. We first develop a new way for getting Landau Ginzburg (LG) CalabiYau threefols W3, embedded in four complex dimensional toric varieties, mirror to sigma model on toric Calabi-Yau threefolds M3. This method gives di...
متن کاملCompactifications of F-Theory on Calabi–Yau Threefolds – II
We continue our study of compactifications of F-theory on Calabi–Yau threefolds. We gain more insight into F-theory duals of heterotic strings and provide a recipe for building F-theory duals for arbitrary heterotic compactifications on elliptically fibered manifolds. As a byproduct we find that string/string duality in six dimensions gets mapped to fiber/base exchange in F-theory. We also cons...
متن کاملClosed Form Expressions for Hodge Numbers of Complete Intersection Calabi-Yau Threefolds in Toric Varieties
We use Batyrev-Borisov’s formula for the generating function of stringy Hodge numbers of Calabi-Yau varieties realized as complete intersections in toric varieties in order to get closed form expressions for Hodge numbers of Calabi-Yau threefolds in five-dimensional ambient spaces. These expressions involve counts of lattice points on faces of associated Cayley polytopes. Using the same techniq...
متن کاملS ep 2 00 0 THE MODULARITY CONJECTURE FOR RIGID CALABI – YAU THREEFOLDS OVER
: We formulate the modularity conjecture for rigid Calabi–Yau threefolds defined over the field Q of rational numbers. We establish the modularity for the rigid Calabi–Yau threefold arising from the root lattice A3. Our proof is based on geometric analysis. 1. The L–series of Calabi–Yau threefolds Let Q be the field of rational numbers, and let Q̄ be its algebraic closure with Galois group G := ...
متن کامل