Diameter bounds for $$\varvec{\text {SL}(2,\mathbb {Z})}$$-orbits of origamis in $$\varvec{\mathcal {H}(2)}$$ and the Prym loci in $$\varvec{\mathcal {H}(4)}$$ and $$\varvec{\mathcal {H}(6)}$$
Year: 2026
Type: article
Abstract: Using algorithms implicit in the classification of $$\text {SL}(2,\mathbb {Z})$$ SL ( 2 , Z ) -orbits of primitive origamis in the stratum $$\mathcal {H}(2)$$ H ( 2 ) due to Hubert–Lelièvre and McMullen, we give diameter bounds on the resulting orbit graphs. Since the machinery of McMullen from $$\mathcal {H}(2)$$ H ( 2 ) is generalised and reused in Lanneau and Nguyen’s classification of the orbits of Prym eigenforms in $$\mathcal {H}(4)$$ H ( 4 ) and $$\mathcal {H}(6)$$ H ( 6 ) , we are also able to obtain diameter bounds for the orbit graphs in this setting as well. In each stratum, we obtain diameter bounds of the form $$O(N^{2/3}\log N)$$ O ( N 2 / 3 log N ) , where N is the size of the orbit graph.
Source: Mathematische Zeitschrift
Authors: Luke Jeffreys, Carlos Matheus
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,290
OpenAlex ID: W7140454192