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Quadratic complete intersections
Journal of Algebra ( IF 0.8 ) Pub Date : 2021-04-01 , DOI: 10.1016/j.jalgebra.2019.11.031
David Eisenbud , Irena Peeva , Frank-Olaf Schreyer

Abstract We study Betti numbers of graded finitely generated modules over a quadratic complete intersection. In the case of codimension 1, we give a natural class of quadratic forms Q whose Clifford algebras are division rings, and deduce the possible Betti numbers of modules over the hypersurfaces Q = 0 . Our approach leads to a new version of the Betti degree Conjecture. In higher codimensions, we obtain formulas for the Betti numbers in terms of the ranks of certain free modules in a higher matrix factorization.

中文翻译:

二次完全交集

摘要 我们研究了二次完全交集上分级有限生成模块的 Betti 数。在余维 1 的情况下,我们给出了一个自然的二次型 Q 类,其 Clifford 代数是除环,并推导出超曲面 Q = 0 上可能的 Betti 模数。我们的方法导致了 Betti 度猜想的新版本。在更高的维度中,我们根据更高矩阵分解中某些自由模块的等级获得 Betti 数的公式。
更新日期:2021-04-01
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