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math.AG2026
On the De Rham Cohomology of Zero-Dimensional Schemes
Martin Kreuzer, Le Ngoc Long
The (naive) de Rham cohomology of a zero-dimensional scheme is the homology of the Kähler differential algebra of its coordinate ring, viewed as a complex. Since it is well-known t…
math.AG2025
Re-Embeddings of Special Border Basis Schemes
Martin Kreuzer, Lorenzo Robbiano
Border basis schemes are open subschemes of the Hilbert scheme of points in an affine space . They have easily describable systems of generators of their vanishin…
math.AG2022
Optimal Re-Embeddings of Border Basis Schemes
Martin Kreuzer, Le Ngoc Long, Lorenzo Robbiano
Border basis schemes are open subschemes of Hilbert schemes parametrizing 0-dimensional subschemes of of given length. They yield open coverings and are easy to desc…