Symbolic Powers and Matroids

By Matteo Varbaro. 2010

60 citations recorded by the source corpus.

We prove that all the symbolic powers of a Stanley-Reisner ideal are Cohen-Macaulay if and only if the associated simplicial complex is a matroid.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/dbdd7fd0374d8f9b58e997ef2aa883af459c03d2

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Juan Migliore
2. Uwe Nagel
3. A. V. Geramita
4. Brian Harbourne
5. Luis N'unez-Betancourt
6. Hailong Dao
7. Naoki Terai
8. A. Stefani

In Computational Theory and Mathematics

1. Uwe Nagel
2. Juan Migliore
3. A. V. Geramita
4. Brian Harbourne
5. Craig Huneke
6. Naoki Terai
7. Ngô Viêt Trung
8. Luis N'unez-Betancourt

In Geometry and Topology

1. Juan Migliore
2. A. V. Geramita
3. Uwe Nagel
4. Brian Harbourne
5. Luis N'unez-Betancourt
6. Hailong Dao
7. A. Stefani
8. Eloísa Grifo

Citations in the corpus

• Star configurations in Pn (2013, background): “We now recall a key fact from [23] and [27]:”
• Matroid configurations and symbolic powers of their ideals (2015, background): “, [1], [2], [3], [5], [6], [7], [10], [14], [15], [16], [17], [23], [27], [28], [30], [31]).”
• Symbolic Powers of Ideals (2015, background): “ry 3.30). In the final section of this survey we discuss the combinatorics that are encoded in the symbolic powers of monomial ideals. First, we discuss the work of Minh and Trung [MT11a], and Varbaro [Var11] which characterizes the Cohen-Macaulayness property of the symbolic powers in terms of the c”
• Cohen-Macaulayness of large powers of Stanley-Reisner ideals (2010, background): “The equivalence (i) ⇔ (v) of the first theorem was discovered in [16, 26].”