For the Hermitian curve H defined over the finite field Fq2, we give a complete classification of Galois coverings of H of prime degree. The corresponding quotient curves turn out to be special cases of wider families of curves Fq2-covered by H arising from subgroups of the special linear group SL(2, Fq) or from subgroups in the normaliser of the Singer group of the projective unitary group PGU...

Yu. I. Manin conjectured that the maximal abelian extensions of real quadratic number fields are generated by pseudo-lattices with multiplication. We prove this conjecture using theory measured foliations on modular curves.

We propose a novel method for curve structure extraction of cartoon images. Our method handles two types of cartoon curves, decorative curves and boundary curves, in a uniform way. The method consists of two steps. First, we calculate curve points by applying non-maximal suppress on secondary derivative of cartoon images. Second, these curve points are linked together to form structure curves w...

We prove that on a punctured oriented surface with Euler characteristic χ < 0, the maximal cardinality of a set of essential simple arcs that are pairwise nonhomotopic and intersecting at most once is 2|χ|(|χ|+1). This gives a cubic estimate in |χ| for a set of curves pairwise intersecting at most once on a closed surface. We also give polynomial estimates in |χ| for sets of arcs and curves pai...