Some Calabi-yau Coverings over Singular Varieties and New Calabi-yau Threefolds with Picard Rank One
نویسنده
چکیده
This paper is a report on the observation that some singular varieties admit Calabi-Yau coverings. We derive a formula for calculating the invariants of the coverings with degeneration methods. By applying these to Takagi’s Q -Fano examples([Ta1], [Ta2]), we construct several Calabi-Yau threefolds with Picard number one. It turns out that at least 22 of them are new.
منابع مشابه
Calabi–yau Coverings over Some Singular Varieties and New Calabi-yau 3-folds with Picard Number One
A Calabi–Yau manifold is a compact Kähler manifold with trivial canonical class such that the intermediate cohomologies of its structure sheaf are all trivial (h(X,OX ) = 0 for 0 < i < dim(X)). One handy way of constructing Calabi–Yau manifolds is by taking coverings of some smooth varieties such that some multiples of their anticanonical class have global sections. Indeed many of known example...
متن کاملPrimitive Calabi-yau Threefolds
A Calabi-Yau threefold is a complex projective threefold X (possibly with some suitable class of singularities, say terminal or canonical) with ω X ∼ = O X and h 1 (O X) = h 2 (O X) = 0. One of the fundamental gaps in the classification of algebraic threefolds is the lack of understanding of Calabi-Yau threefolds. Here I will try to set forth a program to bring the morass of thousands of exampl...
متن کاملAlgebraic topology of Calabi–Yau threefolds in toric varieties
One of the most fruitful sources of Calabi–Yau threefolds is hypersurfaces, or more generally complete intersections, in toric varieties. This is especially true since there is a proposal for the mirror of any such Calabi–Yau threefold. Usually the toric varieties associated to convex lattice polytopes are singular, causing the Calabi–Yau threefolds in them also to be singular, so that to get s...
متن کاملCalabi–yau Construction by Smoothing Normal Crossing Varieties
We investigate a method of construction of Calabi–Yau manifolds, that is, by smoothing normal crossing varieties. We develop some theories for calculating the Picard groups of the Calabi–Yau manifolds obtained in this method. As an application, we construct more than two hundred new families of Calabi–Yau 3-folds with Picard number one that have different Hodge numbers (h’s). We also exhibit a ...
متن کاملCalabi-yau Threefolds of Quotient Type
By a Calabi-Yau threefold we mean a minimal complex projective threefold X such that O X (K X) ' O X and h 1 (O X) = 0. This paper consists of four parts. In Section 1 we formulate an equivariant version of Torelli Theorem of K3 surface with a nite group action and deduce some more geometrical consequences. In Section 2, we classify Calabi-Yau threefolds with innnite fundamental group by means ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2006