Borel-fixed ideals play a key role in the study of Hilbert schemes. Indeed each component and each intersection of components of a Hilbert scheme contains at least one Borel- fixed point, i.e. a point corresponding to a subscheme defiined by a Borel-fixed ideal. Moreover Borel-fixed ideals have good combinatorial properties, which make them very interesting in an algorithmic perspective. In this paper, we propose an implementation of the algorithm computing all the saturated Borel-fixed ideals with number of variables and Hilbert polynomial assigned, introduced from a theoretical point of view in the paper "Segment ideals and Hilbert schemes of points", Discrete Mathematics 311 (2011).

An efficient implementation of the algorithm computing the Borel-fixed points of a Hilbert scheme

Lella, Paolo
2012-01-01

Abstract

Borel-fixed ideals play a key role in the study of Hilbert schemes. Indeed each component and each intersection of components of a Hilbert scheme contains at least one Borel- fixed point, i.e. a point corresponding to a subscheme defiined by a Borel-fixed ideal. Moreover Borel-fixed ideals have good combinatorial properties, which make them very interesting in an algorithmic perspective. In this paper, we propose an implementation of the algorithm computing all the saturated Borel-fixed ideals with number of variables and Hilbert polynomial assigned, introduced from a theoretical point of view in the paper "Segment ideals and Hilbert schemes of points", Discrete Mathematics 311 (2011).
ISSAC 2012 - Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation
9781450312691
Borel-fixed ideals; Hilbert polynomial; Hilbert scheme.
File in questo prodotto:
File Dimensione Formato  
29_final.pdf

accesso aperto

: Publisher’s version
Dimensione 336.77 kB
Formato Adobe PDF
336.77 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/1041680
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 14
  • ???jsp.display-item.citation.isi??? ND
social impact