Deformations of Q-calabi-yau 3-folds and Q-fano 3-folds of Fano Index 1
نویسندگان
چکیده
In this article, we prove that any Q-Calabi-Yau 3-fold with only ordinary terminal singularities and any Q-Fano 3-fold of Fano index 1 with only terminal singularities have Q-smoothings.
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 کاملOn Fano Indices of Q-fano 3-folds
We shall give the best possible upper bound of the Fano indices together with a characterization of those Q-Fano 3-folds which attain the maximum in terms of graded rings. 0. Introduction Q-Fano 3-folds play important roles in birational algebraic geometry. They have been studied by several authors since G. Fano. In this paper, we study Q-Fano 3-folds from the view of their Fano indices (See de...
متن کاملKaori Suzuki
This paper considers Q-Fano 3-folds X with ρ = 1. The aim is to determine the maximal Fano index f of X. We prove that f ≤ 19, and that in case of equality, the Hilbert series of X equals that of weighted projective space P(3, 4, 5, 7). We also consider all possibility of X for f ≥ 9. 0. Introduction We say that X is a Q-Fano variety if it has only terminal singularities, the anticanonical Weil...
متن کامل0 M ay 2 00 5 INTEGRAL COHOMOLOGY AND MIRROR SYMMETRY FOR CALABI - YAU 3 - FOLDS
In this paper we compute the integral cohomology groups for all examples of Calabi-Yau 3-folds obtained from hypersurfaces in 4-dimensional Gorenstein toric Fano varieties. Among 473 800 776 families of Calabi-Yau 3-folds X corresponding to 4-dimensional reflexive polytopes there exist exactly 32 families having non-trivial torsion in H∗(X, Z). We came to an interesting observation that the tor...
متن کاملA holomorphic Casson invariant for Calabi - Yau 3 - folds , and bundles on K 3 fibrations
We briefly review the formal picture in which a Calabi-Yau n-fold is the complex analogue of an oriented real n-manifold, and a Fano with a fixed smooth anticanonical divisor is the analogue of a manifold with boundary, motivating a holomorphic Casson invariant counting bundles on a Calabi-Yau 3-fold. We develop the deformation theory necessary to obtain the virtual moduli cycles of [LT], [BF] ...
متن کامل