Rocky Mountain Journal of Mathematics

The symbolic generic initial system of almost linear point configurations in $\mathbb P^2$

Sarah Mayes

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Abstract

Consider an ideal $I \subseteq K[x,y,z]$ corresponding to a point configuration in $\mathbb {P}^2$ where all but one of the points lies on a single line. In this paper, we study the symbolic generic initial system $\{\rm{gin\,}(I^{(m)})\}_m$ obtained by taking the reverse lexicographic generic initial ideals of the uniform fat point ideals $I^{(m)}$. We describe the limiting shape of $\{\rm{gin\,}(I^{(m)})\}_m$ and, in proving this result, demonstrate that infinitely many of the ideals $I^{(m)}$ are componentwise linear.

Article information

Source
Rocky Mountain J. Math., Volume 46, Number 1 (2016), 283-299.

Dates
First available in Project Euclid: 23 May 2016

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1464035863

Digital Object Identifier
doi:10.1216/RMJ-2016-46-1-283

Mathematical Reviews number (MathSciNet)
MR3506089

Zentralblatt MATH identifier
1356.13036

Subjects
Primary: 13P10: Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)
Secondary: 13C40: Linkage, complete intersections and determinantal ideals [See also 14M06, 14M10, 14M12]

Keywords
Generic initial ideals fat points symbolic powers asymp­totic behavior

Citation

Mayes, Sarah. The symbolic generic initial system of almost linear point configurations in $\mathbb P^2$. Rocky Mountain J. Math. 46 (2016), no. 1, 283--299. doi:10.1216/RMJ-2016-46-1-283. https://projecteuclid.org/euclid.rmjm/1464035863


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