English

The $a$-numbers of Fermat and Hurwitz curves

Number Theory 2016-03-14 v1

Abstract

For an algebraic curve X\mathcal{X} defined over an algebraically closed field of characteristic p>0p >0, the aa-number a(X)a(\mathcal{X}) is the dimension of the space of exact holomorphic differentials on X\mathcal{X}. We compute the aa-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.

Keywords

Cite

@article{arxiv.1603.03604,
  title  = {The $a$-numbers of Fermat and Hurwitz curves},
  author = {Maria Montanucci and Pietro Speziali},
  journal= {arXiv preprint arXiv:1603.03604},
  year   = {2016}
}