منابع مشابه
Multi-degree Bounds on the Betti Numbers of Real Varieties and Semi-algebraic Sets and Applications
We prove new bounds on the Betti numbers of real varieties and semi-algebraic sets that have a more refined dependence on the degrees of the polynomials defining them than results known before. Our method also unifies several different types of results under a single framework, such as bounds depending on the total degrees, on multi-degrees, as well as in the case of quadratic and partially qua...
متن کاملCharacteristic Varieties and Betti Numbers of Free Abelian Covers
The regular Z-covers of a finite cell complex X are parameterized by the Grassmannian of r-planes in H(X,Q). Moving about this variety, and recording when the Betti numbers b1, . . . , bi of the corresponding covers are finite carves out certain subsets Ωr(X) of the Grassmannian. We present here a method, essentially going back to Dwyer and Fried, for computing these sets in terms of the jump l...
متن کاملOn the Complexity of Counting Irreducible Components and Computing Betti Numbers of Algebraic Varieties
This thesis is a continuation of the study of counting problems in algebraic geometry within an algebraic framework of computation started by Bürgisser, Cucker, and Lotz in a series of papers [BC03, BC06, BCL05]. In its first part we give a uniform method for the two problems #CCC and #ICC of counting the connected and irreducible components of complex algebraic varieties, respectively. Our alg...
متن کاملBounds on the individual Betti numbers of complex varieties, stability and algorithms
We prove graded bounds on the individual Betti numbers of affine and projective complex varieties. In particular, we give for each p, d, r, explicit bounds on the p-th Betti numbers of affine and projective subvarieties of Ck and PC, defined by r polynomials of degrees at most d as a function of p, d and r. Unlike previous bounds these bounds are independent of k, the dimension of the ambient s...
متن کاملOn the Betti Numbers of Chessboard Complexes
In this paper we study the Betti numbers of a type of simplicial complex known as a chessboard complex. We obtain a formula for their Betti numbers as a sum of terms involving partitions. This formula allows us to determine which is the first nonvanishing Betti number (aside from the 0-th Betti number). We can therefore settle certain cases of a conjecture of Björner, Lovász, Vrećica, and Z̆ival...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1964
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1964-0161339-9