Proves the conjectured minimal number of generators for licci zero-dimensional monomial ideals or those with small Loewy colength.
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Introduces broken Gorenstein structures that guarantee smoothness on the Hilbert scheme of points on threefolds, with characterizations for monomial ideals and proofs of Hu's conjectures.
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On the number of generators of licci ideals
Proves the conjectured minimal number of generators for licci zero-dimensional monomial ideals or those with small Loewy colength.
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The Hilbert scheme of points on a threefold: broken Gorenstein structures and linkage
Introduces broken Gorenstein structures that guarantee smoothness on the Hilbert scheme of points on threefolds, with characterizations for monomial ideals and proofs of Hu's conjectures.