scholarly journals Segre's regularity bound for fat point schemes

2020 ◽  
Vol 20 (1) ◽  
pp. 217-237
Author(s):  
Uwe Nagel ◽  
Bill Trok
Keyword(s):  
Fat Point

Kähler Differentials for Fat Point Schemes in ℙ1×ℙ1

2021 ◽  
Vol 13 (2) ◽  
Author(s):  
Elena Guardo ◽  
Martin Kreuzer ◽  
Tran N. K. Linh ◽  
Le Ngoc Long
Keyword(s):  
Fat Point ◽  
Kähler Differentials

scholarly journals Fat point embeddings in affine space

2008 ◽  
Vol 212 (7) ◽  
pp. 1583-1593
Author(s):  
Jean-Philippe Furter
Keyword(s):  
Affine Space ◽  
Fat Point

Fat Points in ℙ1× ℙ1and Their Hilbert Functions

2004 ◽  
Vol 56 (4) ◽  
pp. 716-741 ◽  
Author(s):  
Elena Guardo ◽  
Adam Van Tuyl
Keyword(s):  
Finite Number ◽  
Hilbert Function ◽  
Free Resolution ◽  
Hilbert Functions ◽  
Minimal Free Resolution ◽  
Fat Points ◽  
Fat Point ◽  
Point Scheme

AbstractWe study the Hilbert functions of fat points in ℙ1× ℙ1. IfZ⊆ ℙ1× ℙ1is an arbitrary fat point scheme, then it can be shown that for everyiandjthe values of the Hilbert functionHZ(l,j) andHZ(i,l) eventually become constant forl≫ 0. We show how to determine these eventual values by using only the multiplicities of the points, and the relative positions of the points in ℙ1× ℙ1. This enables us to compute all but a finite number values ofHZwithout using the coordinates of points. We also characterize the ACM fat point schemes using our description of the eventual behaviour. In fact, in the case thatZ⊆ ℙ1× ℙ1is ACM, then the entire Hilbert function and its minimal free resolution depend solely on knowing the eventual values of the Hilbert function.

Kähler differentials and Kähler differents for fat point schemes

2015 ◽  
Vol 219 (10) ◽  
pp. 4479-4509 ◽  
Author(s):  
Martin Kreuzer ◽  
N.K. Linh Tran ◽  
Ngoc Long Le
Keyword(s):  
Fat Point ◽  
Kähler Differentials

Classifying Hilbert functions of fat point subschemes in ℙ2

2009 ◽  
Vol 60 (2) ◽  
pp. 159-192 ◽  
Author(s):  
A. V. Geramita ◽  
Brian Harbourne ◽  
Juan Migliore
Keyword(s):  
Hilbert Functions ◽  
Fat Point

scholarly journals Postulation of general quintuple fat point schemes in P3

2012 ◽  
Vol 363 ◽  
pp. 113-139 ◽  
Author(s):  
E. Ballico ◽  
M.C. Brambilla ◽  
F. Caruso ◽  
M. Sala
Keyword(s):  
Fat Point
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