2024
DOI: 10.2140/ant.2024.18.947
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Multiplicity structure of the arc space of a fat point

Rida Ait El Manssour,
Gleb Pogudin

Abstract: The equation x m = 0 defines a fat point on a line. The algebra of regular functions on the arc space of this scheme is the quotient of k[x, x ′ , x (2) , . . . ] by all differential consequences of x m = 0. This infinite-dimensional algebra admits a natural filtration by finite-dimensional algebras corresponding to the truncations of arcs. We show that the generating series for their dimensions equals m/(1 − mt). We also determine the lexicographic initial ideal of the defining ideal of the arc space. These r… Show more

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