-homotopy theory of schemes
A 2-dimensional Algebraic Variety With 27 Rectilinear Generators and 108 Trisecants and its Connection With the Maximal Exceptional Simple lie Group
A 4₃ configuration of lines and conics in ℙ⁵
Studying the connection between the title configuration and Kummer surfaces we write explicit quadratic equations for the latter. The main results are presented in Theorems 8 and 16.
A Barth-Lefschetz type theorem for branched coverings of Grassmannians.
A Barth-Type Theorem for Branched Coverings of Projective Space.
A basis for the non-archimedean holomorphic theta functions.
A Bertini type theorem in analytic geometry.
A Bezout theorem for determinantal modules
A Bogomolov property for curves modulo algebraic subgroups
Generalizing a result of Bombieri, Masser, and Zannier we show that on a curve in the algebraic torus which is not contained in any proper coset only finitely many points are close to an algebraic subgroup of codimension at least . The notion of close is defined using the Weil height. We also deduce some cardinality bounds and further finiteness statements.
A bound for the average rank of a family of abelian varieties
In this note, we consider a one-parameter family of Abelian varieties , and find an upper bound for the average rank in terms of the generic rank. This bound is based on Michel's estimates for the average rank in a one-parameter family of Abelian varieties, and extends previous work of Silverman for elliptic surfaces.
A bound for the degree of smooth surfaces in not of general type
A bound for the Milnor number of plane curve singularities
Let f = 0 be a plane algebraic curve of degree d > 1 with an isolated singular point at 0 ∈ ℂ2. We show that the Milnor number μ0(f) is less than or equal to (d−1)2 − [d/2], unless f = 0 is a set of d concurrent lines passing through 0, and characterize the curves f = 0 for which μ0(f) = (d−1)2 − [d/2].
A bound of the degree of some rational surfaces in .
A bound on the Euler number for certain Calabi-Yau 3-folds.
A bound on the geometric genus of projective varieties
A Bound on the Order of Jumping Lines.
A boundedness theorem for morphisms between threefolds
The main result of this paper is as follows: let be smooth projective threefolds (over a field of characteristic zero) such that . If is not a projective space, then the degree of a morphism is bounded in terms of discrete invariants of and . Moreover, suppose that and are smooth projective -dimensional with cyclic Néron-Severi groups. If , then the degree of is bounded iff is not a flat variety. In particular, to prove our main theorem we show the non-existence of a flat 3-dimensional...
A logarithmic Dolbeault complex
A Cancellation Theorem for Projective Modules in the Metastable Range.
A cartesian closed extension of a category of affine schemes