Calculating Discriminants by Higher Direct Images
نویسندگان
چکیده
منابع مشابه
Section 3.8 - Higher Direct Images of Sheaves
In this note we study the higher direct image functors Rf∗(−) and the higher coinverse image functors Rf (−) which will play a role in our study of Serre duality. The main theorem is the proof that if F is quasi-coherent then so is Rf∗(F ), which we prove first for noetherian schemes and then more generally for quasi-compact quasi-separated schemes. Most proofs are from either Hartshorne’s book...
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1.1. Injective resolutions. Let C be an abelian category. An object I ∈ C is injective if the functor Hom(−, I) is exact. An injective resolution of an object A ∈ C is an exact sequence 0→ A→ I → I → . . . where I• are injective. We say C has enough injectives if every object has an injective resolution. It is easy to see that this is equivalent to saying every object can be embedded in an inje...
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In this paper, we investigate higher direct images of log canonical divisors. After we reformulate Koll ar's torsion-free theorem, we treat the relationship between higher direct images of log canonical divisors and the canonical extensions of Hodge ltration of gradedly polarized variations of mixed Hodge structures. As a corollary, we obtain a logarithmic version of Fujita-Kawamata's semi-posi...
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Using the harmonic theory developed by Takegoshi for representation of relative cohomology and the framework of computation of curvature of direct image bundles by Berndtsson, we prove that the higher direct images by a smooth morphism of the relative canonical bundle twisted by a semi-positive vector bundle are locally free and semi-positively curved, when endowed with a suitable Hodge type me...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1994
ISSN: 0002-9947
DOI: 10.2307/2154537