  We describe the results of a systematic high-statistics Monte-Carlo study of
finite-size effects at the phase transition of compact U(1) lattice gauge
theory with Wilson action on a hypercubic lattice with periodic boundary
conditions. We find unambiguously that the critical exponent nu is lattice-size
dependent for volumes ranging from 4^4 to 12^4. Asymptotic scaling formulas
yield values decreasing from nu(L >= 4) = 0.33 to nu(L >= 9) = 0.29. Our
statistics are sufficient to allow the study of different phenomenological
scenarios for the corrections to asymptotic scaling. We find evidence that
corrections to a first-order transition with nu=0.25 provide the most accurate
description of the data. However the corrections do not follow always the
expected first-order pattern of a series expansion in the inverse lattice
volume V^{-1}. Reaching the asymptotic regime will require lattice sizes
greater than L=12. Our conclusions are supported by the study of many cumulants
which all yield consistent results after proper interpretation.
