Symbolic defect
The following is a list of articles that mention the symbolic defect of an ideal. This notion was defined in [1] below to measure the gap between regular and symbolic powers of ideals. You can download this list as a PDF or BibTeX file.
[1] F. Galetto, A.V. Geramita, Y.S. Shin, and A. Van Tuyl
The symbolic defect of an ideal
J. Pure Appl. Algebra, 223(6):2709--2731, 2019 - arXiv:1610.00176
[2] H. Haghighi and M. Mosakhani
Containment problem for quasi star configurations of points in \(\mathbb P^2\)
Algebra Colloq., 25(4):661--670, 2018 - arXiv:1703.02827
[3] R. Fröberg, S. Lundqvist, A. Oneto, and B. Shapiro
Algebraic stories from one and from the other pockets
Arnold Math. J., 4(2):137--160, 2018 - arXiv:1801.01692
[4] M. Janssen, T. Kamp, and J. Vander Woude
Comparing powers of edge ideals
J. Algebra Appl., 18(10):19, 2019 - arXiv:1709.08701
[5] I. B. Jafarloo and G. Zito
On the containment problem for fat points
J. Commut. Algebra, 13(3):305--321, 2021 - arXiv:1802.10178
[6] B. Drabkin and L. Guerrieri
Asymptotic invariants of ideals with Noetherian symbolic Rees algebra and applications to cover ideals
J. Pure Appl. Algebra, 224(1):300--319, 2020 - arXiv:1802.01884
[7] B. Chakraborty and M. Mandal
Invariants of the symbolic powers of edge ideals
J. Algebra Appl., 19(10):19, 2020 - arXiv:1904.07717
[8] B. Drabkin, E. Grifo, A. Seceleanu, and B. Stone
Calculations involving symbolic powers
J. Softw. Algebra Geom., 9(1):71--80, 2019 - arXiv:1712.01440
[9] K.-N. Lin and Y.-H. Shen
Symbolic powers and free resolutions of generalized star configurations of hypersurfaces
Mich. Math. J., 73(1):33–66, 2023 - arXiv:1912.04448
[10] E. Carlini, H. T. Hà, B. Harbourne, and A. Van Tuyl
Ideals of powers and powers of ideals. Intersecting algebra, geometry, and combinatorics.
Volume 27 of Lecture Notes of the Unione Matematica Italiana. Cham: Springer, 2020
[11] B. Drabkin and L. Guerrieri
On quasi-equigenerated and Freiman cover ideals of graphs
Commun. Algebra, 48(10):4413--4435, 2020 - arXiv:1909.07175
[12] I. B. Jafarloo and G. Malara
Regularity and symbolic defect of points on rational normal curves
Period. Math. Hung., 87(2):508--519, 2023 - arXiv:2007.08612
[13] P. Mantero
The structure and free resolutions of the symbolic powers of star configurations of hypersurfaces
Trans. Am. Math. Soc., 373(12):8785--8835, 2020 - arXiv:1907.08172
[14] J. Biermann, H. de Alba, F. Galetto, S. Murai, U. Nagel, A. O'Keefe, T. Römer, and A. Seceleanu
Betti numbers of symmetric shifted ideals
J. Algebra, 560:312--342, 2020 - arXiv:1907.04288
[15] B. Harbourne, J. Kettinger, and F. Zimmitti
Extreme values of the resurgence for homogeneous ideals in polynomial rings
J. Pure Appl. Algebra, 226(2):16, 2022. Id/No 106811 - arXiv:2005.05282
[16] A. V. Jayanthan, A. Kumar, and V. Mukundan
On the resurgence and asymptotic resurgence of homogeneous ideals
Math. Z., 302(4):2407--2434, 2022 - arXiv:2106.15261
[17] E. C. Moreno, C. Kohne, E. Sarmiento, and A. Van Tuyl
Powers of principal \(Q\)-borel ideals
Can. Math. Bull., 65(3):633--652, 2022 - arXiv:2010.13889
[18] H. T. Hà and P. Mantero
The Alexander-Hirschowitz theorem and related problems
In Commutative algebra. Expository papers dedicated to David Eisenbud on the occasion of his 75th birthday, pages 373--427. Cham: Springer, 2021 - arXiv:2101.09762
[19] K.-N. Lin and Y.-H. Shen
Symbolic powers of generalized star configurations of hypersurfaces
J. Algebra, 593:193--216, 2022 - arXiv:2106.02955
[20] P. Mantero, C. B. Miranda-Neto, U. Nagel
A formula for symbolic powers
[21] M. Mandal and D. K. Pradhan
Symbolic defects of edge ideals of unicyclic graphs
J. Algebra Appl., 22(05):2350099, 2023 - arXiv:2204.05489
[22] T. Reimer
The symbolic defect sequence of edge ideals
PhD Thesis, University of Manitoba, 2022
[23] B. R. Oltsik
Symbolic Defect of Monomial Ideals
[24] R. Burity
On a-fold products ideals of hyperplane arrangements
Bulletin des Sciences Mathématiques, 189:103359, 2023
[25] N. Taghipour, S. Bayati, and F. Rahmati
Comparison of symbolic and ordinary powers of parity binomial edge ideals
Monatshefte für Mathematik, pages 1--16, 2023 - arXiv:2311.03155