A347371 Number of isomorphism types of automorphism groups of Riemann surfaces of genus n.

19, 37, 44, 64, 59, 86, 65, 154, 119, 118, 98, 206, 99, 176, 139, 346, 117, 290, 136, 368, 187, 193, 171, 621, 184, 276, 306, 483, 187, 404, 189, 1014, 255, 332, 253, 880, 205, 381, 341, 1163, 244, 549, 244, 788, 436, 401, 273

Offset

2,1

Comments

This includes subgroups of the full automorphism group.

Breuer's book erroneously gives a(33) = 1013. (See errata.)

References

Thomas Breuer, Characters and automorphism groups of compact Riemann surfaces, Cambridge University Press, 2000, p. 91.

Links

Table of n, a(n) for n=2..48.

Thomas Breuer, Errata et Addenda for Characters and Automorphism Groups of Compact Riemann Surfaces.

Jen Paulhus, Branching data for curves up to genus 48.

Example

The 19 automorphism groups for Riemann surfaces of genus 2 are the trivial group, C2, C3, C4, C2 X C2, C5, C6, S3, Q8, C8, D8, C10, C6 . C2, C2 X C6, D12, QD16, SL_2(3), (C2 X C6) . C2, and GL_2(3). [Breuer, Table 9 on p. 77]

Crossrefs

Cf. A179982, A346293, A347368, A347369, A347370, A347372, A347373.

Sequence in context: A217045 A139313 A272205 * A332756 A245363 A109639

Adjacent sequences: A347368 A347369 A347370 * A347372 A347373 A347374

Keyword

nonn,hard

Author

Eric M. Schmidt, Aug 29 2021

Status

approved