Let be a set of -rational points in over a field of characteristic zero, let be a fat point scheme supported at , and let be the bihomogeneous coordinate ring of . In this paper we investigate the module of Kähler differentials . We describe this bigraded -module explicitly via a homogeneous short exact sequence and compute its Hilbert function in a number of special cases, in particular when the support is a complete intersection or an almost complete intersection in . Moreover, we introduce a Kähler different for and use it to characterize ACM reduced schemes in having the Cayley–Bacharach property.
"Kähler Differentials for Fat Point Schemes in ." J. Commut. Algebra 13 (2) 179 - 207, Summer 2021. https://doi.org/10.1216/jca.2021.13.179