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 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, No. 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, No. 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, No. 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, No. 10, Article ID 1950184, 19 p. (2019) - arXiv:1709.08701 |
| [5] | I. B. Jafarloo and G. Zito On the containment problem for fat points J. Commut. Algebra 13, No. 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, No. 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, No. 10, Article ID 2050184, 19 p. (2020) - arXiv:1904.07717 |
| [8] | B. Drabkin, E. Grifo, A. Seceleanu, and B. Stone Calculations involving symbolic powers J. Softw. Algebra Geom. 9, No. 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, No. 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. Lecture Notes of the Unione Matematica Italiana 27. Cham: Springer. xix, 159 p. (2020) |
| [11] | B. Drabkin and L. Guerrieri On quasi-equigenerated and Freiman cover ideals of graphs Commun. Algebra 48, No. 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, No. 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, No. 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, No. 2, Article ID 106811, 16 p. (2022) - arXiv:2005.05282 |
| [16] | A. V. Jayanthan, A. Kumar, and V. Mukundan On the resurgence and asymptotic resurgence of homogeneous ideals Math. Z. 302, No. 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, No. 3, 633-652 (2022) - arXiv:2010.13889 |
| [18] | H. T. Hà and P. Mantero The Alexander-Hirschowitz theorem and related problems Peeva, Irena (ed.), Commutative algebra. Expository papers dedicated to David Eisenbud on the occasion of his 75th birthday. Cham: Springer. 373-427 (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] | M. Mandal and D. K. Pradhan Symbolic defects of edge ideals of unicyclic graphs J. Algebra Appl. 22, No. 5, Article ID 2350099, 30 p. (2023) - arXiv:2204.05489 |
| [21] | T. Reimer The symbolic defect sequence of edge ideals PhD Thesis, University of Manitoba (2022) |
| [22] | R. Burity On a-fold products ideals of hyperplane arrangements Bull. Sci. Math. 189, Article ID 103359, 20 p. (2023). |
| [23] | N. Taghipour, S. Bayati, and F. Rahmati Comparison of symbolic and ordinary powers of parity binomial edge ideals Monatsh. Math. 203, No. 3, 695-710 (2024) - arXiv:2311.03155 |
| [24] | B. R. Oltsik Symbolic Defect of Monomial Ideals Commun. Algebra 52, No. 9, 3996-4012 (2024) - arXiv:2310.12280 |
| [25] | P. Mantero and V. Nguyen The Structure of Symbolic Powers of Matroids Trans. Am. Math. Soc. 379, No. 6, 3855-3894 (2026) - arXiv:2406.13759 |
| [26] | P. Mantero, C. B. Miranda-Neto, U. Nagel A formula for symbolic powers J. Algebra 658, 1-21 (2024) - arXiv:2112.12588 |
| [27] | I. Jahani and S. Bayati Waldschmidt constant of some classes of hypergraphs AUT Journal of Mathematics and Computing (2024) |
| [28] | J. P. Park and Y.-S. Shin. The symbolic defect and the Waldschmidt constant of a general star configuration in \(\mathbb{P}^n\) J. Korean Math. Soc. 62, No. 3, 485-513 (2025) |
| [29] | A. Banerjee, T. H. Ha, and V. B. Lama. Defect Functions Between Filtrations of Ideals arXiv:2512.14573 |
| [30] | T. Chau, A. Duval, S. Faridi, T. Holleben, S. Morey, and L. Şega Symbolic powers and integral closures via extremal ideals arXiv:2602.05076 |
| [31] | T. Rasheed and W. Yao Defect Antichains and Multigraded Symbolic Defect Series of Edge Ideals under Graph Blow-ups arXiv:2606.29817 |