We use relations in the tautological ring of the moduli spaces Mg,n derived by Pand- haripande, Pixton, and Zvonkine from the Givental formula for the r-spin Witten class in order to obtain some restrictions on the dimensions of the tautological rings of the open moduli spaces Mg,n. In particular, we give a new proof for the result of Looijenga (for n = 1) and Buryak et al. (for n > 2) that dimRg1(Mg,n) 6 n. We also give a new proof of the result of Looijenga (for n = 1) and Ionel (for arbitrary n > 1) that Ri(Mg,n) = 0 for i > g and give some estimates for the dimension of Ri(Mg,n) for i 6 g 2.
The tautological ring of Mg,n via Pandharipande-Pixton-Zvonkine r-spin relations
Lewanski D;
2018-01-01
Abstract
We use relations in the tautological ring of the moduli spaces Mg,n derived by Pand- haripande, Pixton, and Zvonkine from the Givental formula for the r-spin Witten class in order to obtain some restrictions on the dimensions of the tautological rings of the open moduli spaces Mg,n. In particular, we give a new proof for the result of Looijenga (for n = 1) and Buryak et al. (for n > 2) that dimRg1(Mg,n) 6 n. We also give a new proof of the result of Looijenga (for n = 1) and Ionel (for arbitrary n > 1) that Ri(Mg,n) = 0 for i > g and give some estimates for the dimension of Ri(Mg,n) for i 6 g 2.File in questo prodotto:
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