scholarly journals Unexpected hypersurfaces with multiple fat points

2020 ◽  
Author(s):  
Justyna Szpond
Keyword(s):  
Fat Points

scholarly journals On Segre's bound for fat points inPn

2016 ◽  
Vol 220 (6) ◽  
pp. 2307-2323 ◽  
Author(s):  
Edoardo Ballico ◽  
Olivia Dumitrescu ◽  
Elisa Postinghel
Keyword(s):  
Fat Points

Separators of fat points in Pn

2010 ◽  
Vol 324 (7) ◽  
pp. 1492-1512 ◽  
Author(s):  
Elena Guardo ◽  
Lucia Marino ◽  
Adam Van Tuyl
Keyword(s):  
Fat Points

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.

scholarly journals The ideal resolution for generic 3-fat points in P2

2004 ◽  
Vol 187 (1-3) ◽  
pp. 99-128 ◽  
Author(s):  
A. Gimigliano ◽  
M. Idà
Keyword(s):  
Fat Points ◽  
The Ideal

scholarly journals ON THE DEGREE OF CURVES VANISHING AT FAT POINTS WITH EQUAL MULTIPLICITIES

2013 ◽  
Vol 67 (1) ◽  
pp. 17-27
Author(s):  
Nguyen Chanh TU ◽  
Do Trong HOANG
Keyword(s):  
Fat Points

On Generating Series of Classes of Equivariant Hilbert Schemes of Fat Points

2010 ◽  
Vol 10 (3) ◽  
pp. 593-602 ◽  
Author(s):  
S. Gusein-Zade ◽  
I. Luengo ◽  
A. Melle-Hernández
Keyword(s):  
Hilbert Schemes ◽  
Fat Points ◽  
Generating Series
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