Hodge level for weighted complete intersections
نویسندگان
چکیده
منابع مشابه
Hodge Numbers of Complete Intersections
Suppose X is a compact Kähler manifold of dimension n and E is a holomorphic vector bundle. For every p ≤ dim C X we have a sheaf Ω p (E) whose sections are holomorphic (p, 0)-forms with coefficients in E. We set and we define the holomorphic Euler characteristics χ p (X, E) := q≥0 (−1) q h p,q (X, E). It is convenient to introduce the generating function of these numbers χ y (X, E) := p≥0 y p ...
متن کاملOn Beilinson’s Hodge and Tate Conjectures for Open Complete Intersections
In his lectures in [G1], M. Green gives a lucid explanation how fruitful the infinitesimal method in Hodge theory is in various aspects of algebraic geometry. A significant idea is to use Koszul cohomology for Hodge-theoretic computations. The idea originates from Griffiths work [Gri] where the Poincaré residue representation of the cohomology of a hypersurface played a crucial role in proving ...
متن کاملToric complete intersections and weighted projective space
It has been shown by Batyrev and Borisov that nef partitions of reflexive polyhedra can be used to construct mirror pairs of complete intersection Calabi–Yau manifolds in toric ambient spaces. We construct a number of such spaces and compute their cohomological data. We also discuss the relation of our results to complete intersections in weighted projective spaces and try to recover them as sp...
متن کاملEffective Non-vanishing for Fano Weighted Complete Intersections
We show that Ambro–Kawamata’s non-vanishing conjecture holds true for a quasi-smooth WCI X which is Fano or Calabi-Yau, i.e. we prove that, if H is an ample Cartier divisor on X , then |H | is not empty. If X is smooth, we further show that the general element of |H | is smooth. We then verify Ambro–Kawamata’s conjecture for any quasi-smooth weighted hypersurface. We also verify Fujita’s freene...
متن کاملThe generalized Hodge and Bloch conjectures are equivalent for general complete intersections
Recall first that a weight k Hodge structure (L,L) has coniveau c ≤ k2 if the Hodge decomposition of LC takes the form LC = Lk−c,c ⊕ Lk−c−1,c+1 ⊕ . . .⊕ Lc,k−c with Lk−c,c 6= 0. If X is a smooth complex projective variety and Y ⊂ X is a closed algebraic subset of codimension c, then Ker (H(X,Q) → H(X \ Y,Q)) is a sub-Hodge structure of coniveau ≥ c of H(X,Q) (cf. [32, Theorem 7]). The generaliz...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Collectanea Mathematica
سال: 2020
ISSN: 0010-0757,2038-4815
DOI: 10.1007/s13348-019-00276-z