  Locally recoverable (LRC) codes provide ways of recovering erased coordinates
of the codeword without having to access each of the remaining coordinates. A
subfamily of LRC codes with hierarchical locality (H-LRC codes) provides added
flexibility to the construction by introducing several tiers of recoverability
for correcting different numbers of erasures. We present a general construction
of codes with 2-level hierarchical locality from maps between algebraic curves
and specialize it to several code families obtained from quotients of curves by
a subgroup of the automorphism group, including rational, elliptic, Kummer, and
Artin-Schreier curves. We further address the question of H-LRC codes with
availability, and suggest a general construction of such codes from fiber
products of curves. Detailed calculations of parameters for H-LRC codes with
availability are performed for Reed-Solomon- and Hermitian-like code families.
Finally, we construct asymptotically good families of H-LRC codes from curves
related to the Garcia-Stichtenoth tower.
