| Description | Group actions on higher genus curves |
| Status | beta |
| Contact | Jen Paulhus |
| Code | higher_genus_w_automorphisms |
| Collections | passports |
Notes: families collection has been superseded by passports
Todo:
- Add higher genus data.
- Add equations for curves.
- dim: dimension of the family of curves, this is a non-negative integer
- genus: genus of the family of curves, this is a positive integer > 1
- signature: a string representing a list of non-negative integers [g0,m1,...,mr] where g0 is the quotient genus, and the mi represent the orders of the generators of the monodromy group
- r: number of branch points of the cover, positive integer
- g0: quotient genus, this is a non-negative integer
- gen_vectors: generating vector for this action, stored as r lists of positive integers representing permutations
- group: automorphism group, string representing a pair of integers encoding the GAP/Magma group id
- label: label for whole family, string of form 'g.a-b.g0.m1-m2-...-mr' where g is genus, a-b is group, g0 is quotient genus, and m1, ..., mr are remaining r entries in signature
- passport_label: label for the passport (numbered by conjugacy class), string of form 'g.a-b.g0.m1-m2-...-mr.x' where x is a positive integer representing the conjugacy class list, and assigned when the data is initially generated by increasing numeric values of the conjugacy classes
- total_label: label including which generating vector, string of form 'g.a-b.g0.m1-m2-...-mr.x.y' where y is a positive integer representing the particular generating vector for a given refined passport, the value is assigned when the data is initially generated in the order the generating vectors are found
- _id: mongodb generated
- hyperelliptic: True/False whether curve is hyperelliptic
- hyp_involution: hyperelliptic involution (if hyperelliptic), stored as list of positive integers representing a permutation
- cyclic_trigonal: True/False whether curve is cyclic trigonal
- cinv: trigonal automorphism (if cyclic trigonal), sotred as a list of positive intgers representing a permutation
- signH: signature of full action, a string representing a list of positive integers for the action of the full automorphism group of this family
- full_auto: group id for the full automorphism group for this family, as string representing a pair of integers encoding the GAP/Magma group id
- full_label: label for full automorphism group, in same form as label above but for full automorphism group data
- cc: ordered pair of positive integers where first number is which refined passport and second is which generating vector for that conjugacy class list
- con: list of conjugacy classes where the action for this particular refined passport occurs, stored as a string representing a list of positive integers
- eqn: string representing an equation for the family, given in LaTeX notation
- jacobian_decomp: a list, where each element of the list encodes one factor in a decomposition of the corresponding Jacobian variety, each factor is represented by a list of three integers: the first representing the dimension of the factor, the second the number of isogenous copies of that factor, and the third which irreducible complex character of the automorphism group this factor corresponds to
- ndim: integer representing the dimension of the corresponing Shimura variety
- genus - search/browse
- group - search/browse
- hyperelliptic - search/browse
- signature - search/brose
- dim - search/browse
- label - lookup
- passport_label - lookup