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Higher Genus Curves Database

Main Table

hgcwa_genvectors: (NEW) Main data for the pages

Column Type Notes
id bigint ??? self generated by DB
ndim smallint cut?
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 jsonb integer[] 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
realcc integer[] replaced with cc
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 text integer[] 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 jsonb integer numeric store Lehmer code?
eqn text text[] string representing an equation for the family, given in LaTeX notation
cyclic_trigonal boolean True/False whether curve is cyclic trigonal
cinv jsonb integer numeric store Lehmer code? trigonal automorphism (if cyclic trigonal)
genvec jsonb integer[] numeric[] ? 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 text integer[] 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 text text[] 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 smallint integer 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

Statistics

hgcwa_per_group_stats: (NEW) Counts for the per genus list of groups

Column Type Notes
group integer[] text GAP ID encoded as a pair of integers [N,i] text '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_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

OLD Tables (current production tables)

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