Primitive Calabi-Yau threefolds
نویسندگان
چکیده
منابع مشابه
Primitive 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...
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We construct examples of primitive contractions of Calabi–Yau threefolds with exceptional locus being P 1 ×P 1 , P 2 , and smooth del Pezzo surfaces of degrees ≤ 5. We describe the images of these primitive contractions and find their smoothing families. In particular we give a method to compute the Hodge numbers of a generic fiber of the smoothing familly of each Calabi–Yau threefold with one ...
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We investigate the moduli theory of Calabi–Yau threefolds, and using Griffiths’ work on the period map, we derive some finiteness results. In particular, we confirm a prediction of Morrison’s Cone Conjecture.
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If X̃ is a Calabi–Yau threefold defined over Q, and p is a good prime (i.e., a prime such that the reduction of X̃ mod p is nonsingular) then the map Frob∗p : H i ét(X̃,Ql) −→ H i ét(X̃,Ql) on l–adic cohomology induced by the geometric Frobenius morphism gives rise to l–adic Galois representations ρl,i : Gal(Q/Q) −→ GLbi(Ql). If a Calabi–Yau threefold X̃ is rigid (i.e., h(X̃) = 0 or equivalently b(X̃)...
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After Bershadsky-Cecotti-Ooguri-Vafa, we introduce an invariant of Calabi-Yau threefolds, which we call the BCOV invariant and which we obtain using analytic torsion. We give an explicit formula for the BCOV invariant as a function on the compactified moduli space, when it is isomorphic to a projective line. As a corollary, we prove the formula for the BCOV invariant of quintic mirror threefold...
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ژورنال
عنوان ژورنال: Journal of Differential Geometry
سال: 1997
ISSN: 0022-040X
DOI: 10.4310/jdg/1214459799