论文标题
某些Artin Gorenstein环的免费分辨率和Lefschetz属性四
Free resolutions and Lefschetz properties of some Artin Gorenstein rings of codimension four
论文作者
论文摘要
1978年，斯坦利（Stanley）建立了一个Artinian Gorenstein（AG）Ring $ a $ a $的示例，其非偶像$ h $ - vector $（1,13,12,13,1）$。 Migliore-Zanello后来表明，对于规律性$ r = 4 $，Stanley的示例具有最小的Codimension $ c $，用于具有非单偶然的$ H $ -vector的AG戒指。弱Lefschetz属性（WLP）已在Ag环上进行了众多研究。很容易表明，具有非否则$ h $ -vector的AG环没有WLP。在Codimension $ c = 3 $中，人们认为所有AG环都有WLP。对于$ c = 4 $，贡迪姆表明，WLP总是以$ r \ le 4 $持有，并为一个家庭提供了一个家庭，其中任何$ r \ ge 7 $都会在WLP失败的情况下，以$ r = 5 $的ikeda失败的早期示例为基础。在本说明中，我们研究了$ a $的最低免费分辨率，以及与lefschetz Properties（弱和强）的关系，以及Jordan Type的$ C = 4 $和$ r \ le 6 $。
In 1978, Stanley constructed an example of an Artinian Gorenstein (AG) ring $A$ with non-unimodal $H$-vector $(1,13,12,13,1)$. Migliore-Zanello later showed that for regularity $r=4$, Stanley's example has the smallest possible codimension $c$ for an AG ring with non-unimodal $H$-vector. The weak Lefschetz property (WLP) has been much studied for AG rings; it is easy to show that an AG ring with non-unimodal $H$-vector fails to have WLP. In codimension $c=3$ it is conjectured that all AG rings have WLP. For $c=4$, Gondim showed that WLP always holds for $r \le 4$ and gives a family where WLP fails for any $r \ge 7$, building on an earlier example of Ikeda of failure of WLP for $r=5$. In this note we study the minimal free resolution of $A$ and relation to Lefschetz properties (both weak and strong) and Jordan type for $c=4$ and $r \le 6$.
