Characterizations of zero-dimensional complete intersections

Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry - Tập 58 - Trang 93-129 - 2016
Martin Kreuzer1, Le Ngoc Long1,2
1Fakultät für Informatik und Mathematik, Universität Passau, Passau, Germany
2Department of Mathematics, Hue University’s College of Education, Hue, Vietnam

Tóm tắt

Given a 0-dimensional subscheme  $${\mathbb X}$$ of a projective space  $${\mathbb P}^n_K$$ over a field K, we characterize in different ways whether  $${\mathbb X}$$ is the complete intersection of n hypersurfaces. Besides a generalization of the notion of a Cayley–Bacharach scheme, these characterizations involve the Kähler and the Dedekind different of the homogeneous coordinate ring of  $${\mathbb X}$$ or its Artinian reduction. We also characterize arithmetically Gorenstein schemes in novel ways and bring in further tools such as the module of regular differential forms, the fundamental class, and the Jacobian module of  $${\mathbb X}$$ . Throughout we strive to work over an arbitrary base field K and keep the scheme  $${\mathbb X}$$ as general as possible, thereby improving several known characterizations.

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Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry

Tập 58

93-129

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