منابع مشابه
Betti Bounds of Polynomials
We initiate a classification of polynomials f : C → C of degree d having the top Betti number of the general fibre close to the maximum. We find a range in which the polynomial must have isolated singularities and another range where it may have at most one line singularity of general Morse transversal type. Our method uses deformations into particular pencils with non-isolated singularities. 2...
متن کاملCentral Ring Actions and Betti Polynomials
We show that when certain cohomological finiteness conditions hold, then the dimensions of the cohomology groups of modules over a finite dimensional algebra are given by polynomials. This applies in particular to quantum complete intersections, and among these all exterior algebras.
متن کاملL-Betti numbers and their analogues in positive characteristic
In this article, we give a survey of results on L2-Betti numbers and their analogues in positive characteristic. The main emphasis is made on the Lück approximation conjecture and the strong Atiyah conjecture.
متن کاملq-analogues of Ehrhart polynomials
One considers weighted sums over points of lattice polytopes, where the weight of a point v is the monomial q for some linear form λ. One proposes a q-analogue of the classical theory of Ehrhart series and Ehrhart polynomials, including Ehrhart reciprocity and involving evaluation at the q-integers.
متن کاملThe Betti Polynomials of Powers of an Ideal
For an ideal I in a regular local ring or a graded ideal I in the polynomial ring we study the limiting behavior of βi(S/I ) = dimK Tor S i (S/m, S/I ) as k goes to infinity. By Kodiyalam’s result it is known that βi(S/I ) is a polynomial for large k. We call these polynomials the Kodiyalam polynomials and encode the limiting behavior in their generating polynomial. It is shown that the limitin...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 1996
ISSN: 0001-8708
DOI: 10.1006/aima.1996.0047