نتایج جستجو برای: codimension 2 subvarieties
تعداد نتایج: 2528055 فیلتر نتایج به سال:
We show that points in the intersection of the tropicalizations of subvarieties of a torus lift to algebraic intersection points with expected multiplicities, provided that the tropicalizations intersect in the expected dimension. We also prove a similar result for intersections inside an ambient subvariety of the torus, when the tropicalizations meet inside a facet of multiplicity 1. The proof...
Abstract We consider Calabi–Yau n -folds X arising from certain hyperplane arrangements. Using Fu–Vial’s theory of distinguished cycles for varieties with motive abelian type, we show that the subring Chow ring generated by divisors, Chern classes and intersections subvarieties positive codimension injects into cohomology. also prove Voisin’s conjecture , Voevodsky’s smash-nilpotence odd-dimens...
We give the first examples of nef line bundles on smooth projective varieties over finite fields which are not semi-ample. More concretely, we find smooth curves on smooth projective surfaces over finite fields such that the normal bundle has degree zero, but no positive multiple of the curve moves in a family of disjoint curves. This answers questions by Keel and Mumford. The proof uses an obs...
Fix an abelian variety $A_0$ and a non-isotrivial scheme over smooth irreducible curve, both defined the algebraic numbers. Consider union of all images translates fixed finite-rank subgroup $A_0$, also numbers, by subvarieties codimension at least $k$ under isogenies between some fiber scheme. We characterize curves inside which are dominate base curve potentially intersect this set in infinit...
Part I introduced the notion of the projective linking number LinkP(Γ, Z) of a compact oriented real submanifold Γ of dimension 2p− 1 in complex projective n-space P with an algebraic subvariety Z ⊂ P−Γ of codimension p. It is shown here that a basic conjecture concerning the projective hull of real curves in P implies the following result: Γ is the boundary of a positive holomorphic p-chain of...
We show that a Gorenstein subcanonical codimension 3 subscheme Z ⊂ X = P , N ≥ 4, can be realized as the locus along which two Lagrangian subbundles of a twisted orthogonal bundle meet degenerately, and conversely. We extend this result to singular Z and all quasiprojective ambient schemes X under the necessary hypothesis that Z is strongly subcanonical in a sense defined below. A central point...
We give examples of subcanonical subvarieties of codimension 3 in projective n-space which are not Pfaffian, i.e. defined by the ideal sheaf of submaximal Pfaffians of an alternating map of vector bundles. This gives a negative answer to a question asked by Okonek [29]. Walter [36] had previously shown that a very large majority of subcanonical subschemes of codimension 3 in Pn are Pfaffian, bu...
In this paper we generalize the classical Noether-Lefschetz Theorem (see [7], [5]) to arbitrary smooth projective threefolds. More specifically, we prove that given any smooth projective threefold X over complex numbers and a very ample line bundle L on X, there is an integer n0(X,L) such that if n ≥ n0(X,L) then the Noether-Lefschetz locus of the linear system H(X,L) is a countable union of pr...
We provide a bound on the Θ-regularity of an arbitrary reduced and irreducible curve embedded in a polarized abelian variety in terms of its degree and codimension. This is an “abelian” version of Gruson–Lazarsfeld–Peskine’s bound on the Castelnuovo–Mumford regularity of a non-degenerate curve embedded in a projective space. As an application, we provide a Castelnuovo type bound for the genus o...
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