A perfect stratification of M_g for g at most 5

2007/08/25 by Claudio Fontanari, Fontanari, Claudio, Eduard Looijenga +1
Computer Science · Mathematics · #14H10 #32S60 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #math.AG #msc:14H10 #msc:32S60

paper · pdf · doi:10.48550/arxiv.0708.3424

Minor revision; 13 pages

openalex publication_date 2007/08/25 · arxiv created 2008/06/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We find for g at most 5 a stratification of depth g-2 of the moduli space of curves M_g with the property that its strata are affine and the classes of their closures provide a Q-basis for the Chow ring of M_g. The first property confirms a conjecture of one of us. The way we establish the second property yields new (and simpler) proofs of theorems of Faber and Izadi which, taken together, amount to the statement that in this range the Chow ring is generated by the lambda-class.

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