On the smoothness of lexicographic points on Hilbert schemes
| Autor: | Alessio Sammartano, Ritvik Ramkumar |
|---|---|
| Rok vydání: | 2022 |
| Předmět: |
Pure mathematics
Algebra and Number Theory Smoothness (probability theory) Mathematics::Commutative Algebra Lexicographic ideal Polynomial ring Standard graded Hilbert scheme Contrast (music) Mathematics - Commutative Algebra Commutative Algebra (math.AC) Lexicographical order Mathematics - Algebraic Geometry Hilbert scheme 14C05 13F20 13F55 15A75 FOS: Mathematics Point (geometry) Exterior algebra Algebraic Geometry (math.AG) Reducible scheme Lexicographic component Mathematics |
| Zdroj: | Journal of Pure and Applied Algebra. 226:106872 |
| ISSN: | 0022-4049 |
| DOI: | 10.1016/j.jpaa.2021.106872 |
| Popis: | We study the geometry of standard graded Hilbert schemes of polynomial rings and exterior algebras. Our investigation is motivated by a famous theorem of Reeves and Stillman for the Grothendieck Hilbert scheme, which states that the lexicographic point is smooth. By contrast, we show that, in standard graded Hilbert schemes of polynomial rings and exterior algebras, the lexicographic point can be singular, and it can lie in multiple irreducible components. We answer questions of Peeva-Stillman and of Maclagan-Smith. Comment: 13 pages. To appear on Journal of Pure and Applied Algebra |
| Databáze: | OpenAIRE |
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