Monodromy and betti numbers of weighted complete intersections
نویسندگان
چکیده
منابع مشابه
Powers of Complete Intersections: Graded Betti Numbers and Applications
Abstract. Let I = (F1, . . . , Fr) be a homogeneous ideal of the ring R = k[x0, . . . , xn] generated by a regular sequence of type (d1, . . . , dr). We give an elementary proof for an explicit description of the graded Betti numbers of Is for any s ≥ 1. These numbers depend only upon the type and s. We then use this description to: (1) write HR/Is , the Hilbert function of R/Is, in terms of HR...
متن کاملMonodromy of Complete Intersections and Surface Potentials
Following Newton, Ivory and Arnold, we study the Newtonian potentials of algebraic hypersurfaces in R. The ramification of (analytic continuations of) these potential depends on a monodromy group, which can be considered as a proper subgroup of the local monodromy group of a complete intersection (acting on a twisted vanishing homology group if n is odd). Studying this monodromy group we prove,...
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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 ...
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We investigate decompositions of Betti diagrams over a polynomial ring within the framework of Boij–Söderberg theory. That is, given a Betti diagram, we decompose it into pure diagrams. Relaxing the requirement that the degree sequences in such pure diagrams be totally ordered, we are able to define a multiplication law for Betti diagrams that respects the decomposition and allows us to write a...
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...
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ژورنال
عنوان ژورنال: Topology
سال: 1985
ISSN: 0040-9383
DOI: 10.1016/0040-9383(85)90009-6