In this paper, we explicitly determine the automorphism group of every nonhyperelliptic superspecial curve of genus $4$ over $\mathbb{ F}_{ 11}$. Our algorithm determining automorphism groups works for any nonhyperelliptic curves of genus $4$ over finite fields. With this computation, we show the compatibility between the enumeration of superspecial curves of genus $4$ over $\mathbb{ F}_{ 11}$ obtained computationally by the first and second authors in 2017 and an enumeration by Galois cohomology theory.
Categories: math.AG