Freeness versus maximal global Tjurina number for plane curves

Global Forcing Number for Maximal Matchings under Graph Operations

Let $S= \{e_1,\,e_2‎, ‎\ldots,\,e_m\}$ be an ordered subset of edges of a connected graph $G$‎. ‎The edge $S$-representation of an edge set $M\subseteq E(G)$ with respect to $S$ is the‎ ‎vector $r_e(M|S) = (d_1,\,d_2,\ldots,\,d_m)$‎, ‎where $d_i=1$ if $e_i\in M$ and $d_i=0$‎ ‎otherwise‎, ‎for each $i\in\{1,\ldots‎ , ‎k\}$‎. ‎We say $S$ is a global forcing set for maximal matchings of $G$‎ ‎if $...

Plane Maximal Curves

We are interested in non-singular plane curves whose number of rational points attains the Hasse-Weil upper bound. Dedicated with affection to J.W.P. Hirschfeld and G. Korchmáros

MILNOR NUMBER EQUALS TJURINA NUMBER FOR FUNCTIONS ON SPACE CURVES Year of publication: 2001 Link to published version: http://dx.doi.org/10.1112/S0024610700001320 Publisher statement: None MILNOR NUMBER EQUALS TJURINA NUMBER FOR FUNCTIONS ON SPACE CURVES

Real Plane Algebraic Curves with Asymptotically Maximal Number of Even Ovals

It is known for a long time that a nonsingular real algebraic curve of degree 2k in the projective plane cannot have more than 7k 2 2 − 9k 4 + 3 2 even ovals. We show here that this upper bound is asymptotically sharp, that is to say we construct a family of curves of degree 2k such that p k →k→∞ 7 4 , where p is the number of even ovals of the curves. We also show that the same kind of result ...

A note on superspecial and maximal curves

In this note we review a simple criterion, due to Ekedahl, for superspecial curves defined over finite fields.Using this we generalize and give some simple proofs for some well-known superspecial curves.