Smooth Hilbert schemes: Their classification and geometry-Reference-Cited by-同舟云学术

Smooth Hilbert schemes: Their classification and geometry

Published:2022-11-29 Issue:0 Volume:0 Page:
ISSN:0075-4102
Container-title:Journal für die reine und angewandte Mathematik (Crelles Journal)
language:en
Short-container-title:

Author:

Skjelnes Roy¹,Smith Gregory G.²

Affiliation:

1. Department of Mathematics , Royal Institute of Technology (KTH) , Stockholm , 100 44 , Sweden

2. Department of Mathematics and Statistics , Queen’s University , Kingston , Ontario, K7L 3N6 , Canada

Abstract

Abstract Closed subschemes in projective space with a fixed Hilbert polynomial are parametrized by a Hilbert scheme. We classify the smooth ones. We identify numerical conditions on a polynomial that completely determine when the Hilbert scheme is smooth. We also reinterpret these smooth Hilbert schemes as generalized partial flag varieties and describe the subschemes being parametrized.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/crelle-2022-0083/pdf

Reference29 articles.

1. A. Beauville, Variétés Kähleriennes dont la première classe de Chern est nulle, J. Differential Geom. 18 (1983), no. 4, 755–782.

2. W. Bruns and J. Herzog, Cohen–Macaulay rings, Cambridge Stud. Adv. Math. 39, Cambridge University, Cambridge 1993.

3. J. Cheah, Cellular decompositions for nested Hilbert schemes of points, Pacific J. Math. 183 (1998), no. 1, 39–90.

4. D. Chen, I. Coskun and S. Nollet, Hilbert scheme of a pair of codimension two linear subspaces, Comm. Algebra 39 (2011), no. 8, 3021–3043.

5. P. Ellia, A. Hirschowitz and E. Mezzetti, On the number of irreducible components of the Hilbert scheme of smooth space curves, Internat. J. Math. 3 (1992), no. 6, 799–807.

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