A necessary condition for an edge ring to satisfy Serre’s condition (\(S_2\)). (English) Zbl 1411.13034

Higashitani, Akihiro; Kimura, Kyouko

Hibi, Takayuki (ed.), The 50th anniversary of Gröbner bases. Proceedings of the 8th Mathematical Society of Japan-Seasonal Institute (MSJ-SI 2015), Osaka, Japan, July 1–10, 2015. Tokyo: Mathematical Society of Japan (MSJ). Adv. Stud. Pure Math. 77, 121-128 (2018).

Summary: Let \(G\) be a finite simple connected graph. We give a necessary condition for the edge ring of \(G\) to satisfy Serre’s condition \((S_2)\) in terms of a graph.
For the entire collection see [Zbl 1404.13003].

MSC:

13H10

Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.)

Keywords:

Serre’s condition (\(S_2\)); edge ring; toric ideal; finite graph