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no. 3
Resurgence numbers and convex regions associated to pairs of graded families of ideals
Hà, Tài Huy1; Jayanthan, A.V.2; Kumar, Arvind3; Nguyễn, Thái Thành4
1Tulane University, Department of Mathematics, 6823 St. Charles Ave., New Orleans, LA 70118, USA
2Department of Mathematics, I.I.T. Madras, Chennai - 600036, INDIA
3Department of Mathematical Sciences, New Mexico State University, 1305 Frenger St, Las Cruces, NM 88001, USA
4Department of Mathematics, University of Dayton, 300 College Park, Dayton, OH 45469, USA
Algebraic Combinatorics, Volume 9 (2026) no. 3, pp. 649-663

We discuss how to understand the asymptotic resurgence number of a pair of graded families of ideals from combinatorial data of their associated convex regions. When the families consist of monomial ideals, the convex regions being considered are the Newton–Okounkov regions of the families. When ideals in the second family are classical invariant ideals, for instance, determinantal ideals or ideals of Pfaffians, these convex regions are constructed from the associated Rees packages.

Received:
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Accepted:
Published online:
DOI: 10.5802/alco.494
Classification: 13A18, 13F20, 13A30
Keywords: family of ideals, resurgence number, asymptotic resurgence, convex body, convex region, Newton polyhedron, monomial ideals

Hà, Tài Huy  1 ; Jayanthan, A.V.  2 ; Kumar, Arvind  3 ; Nguyễn, Thái Thành  4

1 Tulane University, Department of Mathematics, 6823 St. Charles Ave., New Orleans, LA 70118, USA
2 Department of Mathematics, I.I.T. Madras, Chennai - 600036, INDIA
3 Department of Mathematical Sciences, New Mexico State University, 1305 Frenger St, Las Cruces, NM 88001, USA
4 Department of Mathematics, University of Dayton, 300 College Park, Dayton, OH 45469, USA
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
Hà, Tài Huy; Jayanthan, A.V.; Kumar, Arvind; Nguyễn, Thái Thành. Resurgence numbers and convex regions associated to pairs of graded families of ideals. Algebraic Combinatorics, Volume 9 (2026) no. 3, pp. 649-663. doi: 10.5802/alco.494
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