We give an explicit recursive description of the Hilbert series and Gröbner bases for the family of quadratic ideals defining the jet schemes of a double point. We relate these recursions to the Rogers–Ramanujan identity and prove a conjecture of the second author, Oblomkov and Rasmussen.

中文翻译：

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二次理想与Rogers–Ramanujan递归

我们为定义双点喷射方案的二次理想族给出了希尔伯特级数和Gröbner基的明确递归描述。我们将这些递归与Rogers-Ramanujan的身份相关联，并证明第二作者Oblomkov和Rasmussen的猜想。