ERRATUM TO: DISCONTINUOUS GROUPS IN POSITIVE CHARACTERISTIC AND AUTOMORPHISMS OF MUMFORD

The following corrections only affect use of methods from the paper in later work, not the paper itself. Correction 1. The statement of Remark (6.12) for p = 2 is not correct if g = 4. The following should be added: if g = 4 or g = 9, then F (g) = 12(g − 1), so if µ = 112 in such a case, then the corresponding N attains the bound. Inspection of the cases in §5 and §6 of the paper reveal that this only happens for case (A1”) with t1 = 0, t2 = 2, n = 3, and then p = 2 and N ∼ = E2 ∗E1 D3. Correction 1 implies that the following should be added to the statement of the main theorem in [2]: However, if p = 2 and g = 4, there is one more one-parameter family of curves that attains the maximal number F (g) = 36 automor-phisms, namely a family of D3 × D3-covers of P1 (Indeed, the group N of the correction admits only one surjective homomorphism onto a group of order 36, namely N → D3 ×D3, with free kernel Γ of rank four). Correction 1 also has the following effect on [1]. In the main theorem, the statement “p> 3 ” should be left out. Indeed, in the proof of proposition 1.2 of that source, the second sentence should be completed as follows: except if p = 2 and N ∼ = D3∗Z/2D2, which gives rise to the branch type (4, 3), and the statement of that proposition should be corrected accordingly. However, the equation in proposition A is not valid in characteristic two. Correction 2. In Proposition 2, the statement that p 6 = 2, 5 should be left out. The reason is that A5 ∼ = PSL(2, 4) ∼ = PSL(2, 5) does occur in the list of theorem (2.9) in those characteristics. This has the following effect on [1]. In the main theorem, the condition “p 6 = 5” should be left out in case (b). Andreas Schweizer has pointed out that certain Drinfeld modular curves give counterexamples to the original statements in [2] and [1]: over F2(T), the Drinfeld modular curves X(T (T + 1)), X(T 2 +T + 1) and X(T 2) have respective genera 4, 6 and 5 and automorphism groups D3 ×D3, A5 and a group of order 48. They are now covered by the corrections