Gauss maps with nontrivial separable degree in positive characteristic

Separable Endomorphisms of Surfaces in Positive Characteristic

The structure of non-singular projective surfaces admitting non-isomorphic surjective separable endomorphisms is studied in the positive characteristic case. The case of characteristic zero is treated in [2], [16] (cf. [3]). Many similar classification results are obtained also in this case; on the other hand, some examples peculiar to the positive characteristic are given explicitly.

Curves Whose Secant Degree Is One in Positive Characteristic

Here we study (in positive characteristic) integral curves X ⊂ Pr with secant degree one, i.e., for which a general P ∈ Seck−1(X) is in a unique k-secant (k − 1)-dimensional linear subspace.

Modified Gauss Elimination Technique for Separable Nonlinear Programming Problem

Foliations with Degenerate Gauss Maps on P

We obtain a classification of codimension one holomorphic foliations on P with degenerate Gauss maps.

Order of Gauss periods in large characteristic ∗ †

Let p be the characteristic of Fq and let q be a primitive root modulo a prime r = 2n + 1. Let β ∈ Fq2n be a primitive rth root of unity. We prove that the multiplicative order of the Gauss period β + β−1 is at least (log p)c logn for some c > 0. This improves the bound obtained by Ahmadi, Shparlinski and Voloch when p is very large compared with n. We also obtain bounds for ”most” p.