Star-Configurations in 2 Having Generic Hilbert Function and the Weak Lefschetz Property

摘要

We prove that a star-configuration in 2 is defined by general forms of degrees ≤2 if and only if has generic Hilbert function. We also show that if and are star-configurations in 2 defined by general forms of degrees ≤2 and σ() ≠ σ(), then the ring R/(I  + I ) has the Weak Lefschetz property. These two results generalize results of Ahn and Shin [33. Ahn , J. , Shin , Y. S. ( 2012 ). The minimal free resolution of a star-configuration in n and the weak lefschetz property . J. Korean Math. Soc. 49 ( 2 ): 405 - 417 .View all references]. Furthermore, we find the Lefschetz element of the graded Artinian ring R/(I  + I ) precisely when and are two star-configurations in 2 defined by general forms F ₁,…, F _s , and G ₁,…, G _s , L, respectively, with deg F _i  = deg G _i  = 2 for every i ≥ 1, and deg L = 1 with s ≥ 3.View full textDownload full textKey WordsHilbert functions, Minimal free resolutions, Lefschetz elements, Star-Configurations, Weak Lefschetz Property2010 Mathematics Subject ClassificationPrimary 13P25, Secondary 14Q99Related var addthis_config = { ui_cobrand: "Taylor & Francis Online", services_compact: "citeulike,netvibes,twitter,technorati,delicious,linkedin,facebook,stumbleupon,digg,google,more", pubid: "ra-4dff56cd6bb1830b" }; Add to shortlist Link Permalink http://dx.doi.org/10.1080/00927872.2012.656783