Effective Genericity, Δ-regularity and Strong Noether Position
نویسنده
چکیده
We show that the concept of strong Noether position for a polynomial ideal I CP is equivalent to δ-regularity and thus related to Pommaret bases. In particular, we provide explicit Pommaret bases for two of the ideal sequences used in Hashemi’s definition of strong Noether position and alternative proofs for a number of his statements. Finally, we show that one consequence of δ-regularity is that any Pommaret basis contains a system of parameters and we present an algorithm for checking whether the factor ring P/I is Gorenstein via a socle computation.
منابع مشابه
Regularity Results for Families of Nodal Curves on Smooth Projective Threefolds and Postulation of Nodes
Given X a smooth projective threefold, E a rank-two vector bundle on X and k, δ two positive integers, we determine effective and uniform upper-bounds for δ, which are linear polynomials in k, such that the family Vδ(E(k)), parametrizing irreducible and δ-nodal curves which are zero-loci of global sections of the vector bundle E(k) on X, is smooth and of the expected dimension (regular, for sho...
متن کاملInequality in Dimension 3
Among complex smooth projective threefolds with ample canonical divisor K, the Noether inequality is of the form K ≥ 4 3 pg − δ 3 where pg denotes the geometric genus of the threefold and δ is certain number in {10, 12, 14}. Introduction Suppose S is a smooth minimal projective surface of general type. It is well known that M. Noether ([N]) proved the inequality K S ≥ 2pg − 4 whence K 2 S ≥ 2χ−...
متن کاملThe Extender Algebra and Vagaries of Σ 21 Absoluteness Philipp
We review the construction of the extender algebra, a Boolean algebra which is due to Woodin, with δ-many generators. The resulting genericity iteration is applied to prove a new Σ1-absoluteness theorem for c.c.c. forcings with ordinal parameters. Additionally we introduce and discuss sets that extend to a class with unique condensation. We analyse the sets that extend to classes with unique co...
متن کاملStrong Topological Regularity and Weak Regularity of Banach Algebras
In this article we study two different generalizations of von Neumann regularity, namely strong topological regularity and weak regularity, in the Banach algebra context. We show that both are hereditary properties and under certain assumptions, weak regularity implies strong topological regularity. Then we consider strong topological regularity of certain concrete algebras. Moreover we obtain ...
متن کاملTheta-regularity of Curves and Brill–noether Loci
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...
متن کامل