hgcwa_genvectors
: (NEW) Main data for the pages
Column | Type | Notes |
---|---|---|
jacobian_decomp | jsonb | a list consisting of lists of integers, each one of which codes a factor in a Jacobian variety decomposition. An entry [a,b,c] means the factor is b copies of a dimension a variety, where the decomposition comes from a particular character from the automorphism group (labeled by c) |
cc | what used to be realcc, end label for each passport, ordered pair of positive integers where first number is which refined passport and second is which generating vector for that conjugacy class list | |
passport_label | text | 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 | text | 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 |
label | text | 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 |
group | text | automorphism group stored as N.i to match abstract group db. N is order, i is GAP ID or |
full_auto | text | group id for the full automorphism group for this family, as string representing a pair of integers encoding the GAP/Magma group id |
signH | string of integers representing the sign of the full automorphism group | |
hyperelliptic | boolean | True/False whether curve is hyperelliptic |
full_label | text | label for full automorphism group, in same form as label but for full automorphism group data |
hyp_involution | store Lehmer code? | |
eqn | string representing an equation for the family, given in LaTeX notation | |
cyclic_trigonal | boolean | True/False whether curve is cyclic trigonal |
cinv | store Lehmer code? trigonal automorphism (if cyclic trigonal) | |
genvec | ? Store each permutation as integer a la Lehmer codes? generating vector for this action, stored as r lists of positive integers representing permutations | |
g0 | smallint | quotient genus, this is a non-negative integer |
dim | smallint | dimension of the family of curves, this is a non-negative integer |
group_order | integer | order of the group |
r | smallint | number of branch points of the cover, non-negative integer |
signature | 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 | |
genus | smallint | genus of the family of curves, this is a positive integer > 1 |
con | labels connected to abstract db | |
braid | integer[] | ordered pair of positive integers designating the "cc" entry for the generating vector which is the representative for the orbit under braid action which the given generating vector falls into |
topological | integer[] | number of distinct generating vectors, up to topological equivalence, for this genus and group (if g0_is_gt0 is false) |
connected_genvec | text[] | generating vectors listed as products of generators from abstract groups db |
trans_group | text | if nonabelian or abelian and of order <=47, smallest transitive group nTt from Galois group db, NULL if abelian and order >48 or nonabelian and not in db |
min_deg | if nonabelian and in Galois group db, the n from trans_group else NULL, if abelian the order of the group, i.e. smallest transitive degree |
hgcwa_per_group_stats
: (NEW) Counts for the per genus list of groups
Column | Type | Notes |
---|---|---|
group | GAP ID encoded as [N,i] N is the order of the group and i distinguishes groups of the same order (as determined in GAP or the gps_groups table) |
|
genus | smallint | genus |
g0_is_gt0 | boolean | whether the group is for quotient genus 0 or quotient genus >= 1 |
g0_gt0_list | integer[] | list of g0 values this group appears for, if greater than 0 |
gen_vectors | integer | number of distinct generating vectors, up to simultaneous conjugation, for this genus and group |
topological | integer | number of distinct generating vectors, up to topological equivalence, for this genus and group (if g0_is_gt0 is false) |
braid | integer | number of distinct generating vectors, up to braid equivalence, for this genus and group (if g0_is_gt0 is false) |
hgcwa_per_genus_stats
: (NEW) for each genus, list if contains data for quotient genus >0 and whether braid and topological have been computed for that genus. Also totals for distinct families, refined passports, and generating vectors for statistics tables.
Column | Type | Notes |
---|---|---|
genus | smallint | genus |
g0_gt0_compute | boolean | whether quotient genus >0 data has been computed for this genus |
top_braid_compute | boolean | whether topological and braid equivalences have been computed for this genus and g0=0 |
top_braid_g0_gt0 | boolean | False for now (whether topological and braid equivalences have been computed for g0>0) |
nonabelian_only (NEW) | boolean | whether only nonabelian groups have been computed or all groups |
num_families | integer[] | 1st entry is number of distinct families for this genus total, nth entry is for quotient genus n-2 |
num_refined_pp | integer[] | 1st entry is number of distinct refined passports for this genus, nth entry is for quotient genus n-2 |
num_gen_vectors | integer[] | 1st entry is number of distinct generating vectors for this genus, nth entry is for quotient genus n-2 |
num_unique_groups | integer | number of distinct groups of this genus |
hgcwa_passports
: (OLD) Main data for the pages
Column | Type | Notes |
---|---|---|
id | bigint | |
ndim | smallint | |
jacobian_decomp | jsonb | |
cc | jsonb | |
full_auto | text | |
passport_label | text | |
group | text | |
signH | text | |
label | text | |
hyp_involution | jsonb | |
full_label | text | |
eqn | jsonb | |
cinv | jsonb | |
hyperelliptic | boolean | |
gen_vectors | jsonb | |
total_label | text | |
g0 | smallint | |
dim | smallint | |
group_order | integer | |
cyclic_trigonal | boolean | |
r | smallint | |
signature | text | |
genus | smallint | |
con | text | |
braid | integer[] | |
topological | integer[] | |
realcc | integer[] |
hgcwa_unique_groups
: Counts for the per genus list of groups
Column | Type | Notes |
---|---|---|
group | integer[] | GAP ID encoded as a pair of integers [N,i] , where N is the order of the group and i distinguishes groups of the same order (as determined in GAP or the gps_groups table) |
genus | smallint | genus |
g0_is_gt0 | boolean | whether the group is for quotient genus 0 or quotient genus >= 1 |
g0_gt0_list | integer[] | list of g0 values this group appears for, if greater than 0 |
gen_vectors | integer | number of distinct generating vectors, up to simultaneous conjugation, for this genus and group |
topological | integer | number of distinct generating vectors, up to topological equivalence, for this genus and group (if g0_is_gt0 is false) |
braid | integer | number of distinct generating vectors, up to braid equivalence, for this genus and group (if g0_is_gt0 is false) |
hgcwa_complete
: for each genus, list if contains data for quotient genus >0 and whether braid and topological have been computed for that genus. Also totals for distinct families, refined passports, and generating vectors for statistics tables.
Column | Type | Notes |
---|---|---|
genus | smallint | genus |
g0_gt0_compute | boolean | whether quotient genus >0 data has been computed for this genus |
top_braid_compute | boolean | whether topological and braid equivalences have been computed for this genus and g0=0 |
top_braid_g0_gt0 | boolean | False for now (whether topological and braid equivalences have been computed for g0>0) |
nonabelian_only (NEW) | boolean | whether only nonabelian groups have been computed or all groups |
num_families | integer[] | 1st entry is number of distinct families for this genus total, nth entry is for quotient genus n-2 |
num_refined_pp | integer[] | 1st entry is number of distinct refined passports for this genus, nth entry is for quotient genus n-2 |
num_gen_vectors | integer[] | 1st entry is number of distinct generating vectors for this genus, nth entry is for quotient genus n-2 |