Regina Lectures on Fat Points

Connections Between Algebra, Combinatorics, and Geometry - Springer Proceedings in Mathematics & Statistics ◽

10.1007/978-1-4939-0626-0_3 ◽

2014 ◽

pp. 147-187 ◽

Cited By ~ 1

Author(s):

Susan M. Cooper ◽

Brian Harbourne

Keyword(s):

Fat Points

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On Segre's bound for fat points inPn

Journal of Pure and Applied Algebra ◽

10.1016/j.jpaa.2015.11.008 ◽

2016 ◽

Vol 220 (6) ◽

pp. 2307-2323 ◽

Cited By ~ 1

Author(s):

Edoardo Ballico ◽

Olivia Dumitrescu ◽

Elisa Postinghel

Keyword(s):

Fat Points

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New methods for determining speciality of linear systems based at fat points in Pn

Journal of Pure and Applied Algebra ◽

10.1016/j.jpaa.2012.09.019 ◽

2013 ◽

Vol 217 (5) ◽

pp. 927-945 ◽

Cited By ~ 2

Author(s):

Stepan Paul

Keyword(s):

Linear Systems ◽

Fat Points ◽

New Methods

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Separators of fat points in Pn

Journal of Algebra ◽

10.1016/j.jalgebra.2010.07.008 ◽

2010 ◽

Vol 324 (7) ◽

pp. 1492-1512 ◽

Cited By ~ 7

Author(s):

Elena Guardo ◽

Lucia Marino ◽

Adam Van Tuyl

Keyword(s):

Fat Points

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ON THE SEGRE UPPER BOUND OF THE REGULARITY FOR FAT POINTS IN $\mathbb {P}^4$, II

International Journal of Pure and Apllied Mathematics ◽

10.12732/ijpam.v102i2.11 ◽

2015 ◽

Vol 102 (2) ◽

Author(s):

E. Ballico

Keyword(s):

Upper Bound ◽

Fat Points

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Fat Points in ℙ1× ℙ1and Their Hilbert Functions

Canadian Journal of Mathematics ◽

10.4153/cjm-2004-033-0 ◽

2004 ◽

Vol 56 (4) ◽

pp. 716-741 ◽

Cited By ~ 15

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.

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