The a-numbers of Fermat and Hurwitz curves
Copyright policy )The a-numbers of Fermat and Hurwitz curves
For an algebraic curve $\mathcal{X}$ defined over an algebraically closed field of characteristic $p >0$, the $a$-number $a(\mathcal{X})$ is the dimension of the space of exact holomorphic differentials on $\mathcal{X}$. We compute the $a$-number for an infinite families of Fermat and Hurwitz curves. Our results apply to Hermitian curves giving a new proof for a previous result of Gross.
- University of Basilicata Italy
Curves over finite and local fields, Finite ground fields in algebraic geometry, Mathematics - Number Theory, FOS: Mathematics, Arithmetic ground fields for curves, Number Theory (math.NT)
Curves over finite and local fields, Finite ground fields in algebraic geometry, Mathematics - Number Theory, FOS: Mathematics, Arithmetic ground fields for curves, Number Theory (math.NT)
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