Minimal generating set conjecture for the integral Chow ring of the moduli stack of maps

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Let rr be a positive integer and dd a positive odd number. The classes 4c1,c244c_1,c_24 generate the polynomial ring describing the presentation, and let 4α1,0,α1,1,αp,044\alpha_{1,0},\alpha_{1,1},\alpha_{p,0}4 denote the relations defined in the paper, where pp ranges over primes dividing dd. Minimal generating set conjecture.

A∗(M0(Pr,d))≅Z[c1,c2](α1,0,α1,1,{αp,0∣p is a prime that divides d}).A^*\left(\mathcal M_{0}\left(\mathbb P^r,d\right)\right)\cong \frac{\mathbb Z[c_1,c_2]}{\left(\alpha_{1,0},\alpha_{1,1},\{\alpha_{p,0}\mid p\text{ is a prime that divides }d\}\right)}.

Further, all the displayed relations are necessary, so they form a minimal set of generators for the ideal of relations. This conjecture refines the paper's presentation by removing redundant generators; it is motivated by computations, including the case of plane cubics, and remains unresolved in the supplied source.

References

Primary source

Renzo Cavalieri and Damiano Fulghesu, “The integral Chow ring of M_0(P^r, d), for d odd”, arXiv:2201.10697 (2022).

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