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 arXiv:2112.12588 |
| [21] | M. Mandal and D. K. Pradhan Symbolic defects of edge ideals of unicyclic graphs J. Algebra Appl., 22(5):30, 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 arXiv:2310.12280 |
| [24] | R. Burity On a-fold products ideals of hyperplane arrangements Bull. Sci. Math., 189:20, 2023 |
| [25] | N. Taghipour, S. Bayati, and F. Rahmati Comparison of symbolic and ordinary powers of parity binomial edge ideals Monatsh. Math., 203(3):695--710, 2024 - arXiv:2311.03155 |
| [26] | P. Mantero and V. Nguyen The Structure of Symbolic Powers of Matroids arXiv:2406.13759 |