arXiv subjects

Hana Melanova

Publications and source records attributed to Hana Melanova.

2 recordsLinked to original sources

arXiv2021

Geometric Invariants of Plane and Space Curves

The traditional study of plane and space algebraic curves by looking at their tangent vectors, curvatures and torsions provides geometric, but unfortunately not sufficient information about individual curves in order to be able to distinguish between two different ones. The aim of this note is to generalize the classical concept of curvature and torsion to so-called higher algebraic curvatures and to show that each analytic branch of a complex curve is already uniquely defined by them.

math.AG↗

arXiv2020

On the First Fundamental Theorem for $\operatorname{GL}_2(K)$ and $\operatorname{SL}_2(K)$

The First Fundamental Theorem of Invariant Theory describes a minimal generating set of the invariant polynomial ring under the action of some group $G$. In this note we give an elementary and direct proof for the $\operatorname{GL}_2(K)$ and $\operatorname{SL}_2(K)$ for any infinite field $K$. Our proof can be generalized to $\operatorname{GL}_m(K)$ and $\operatorname{SL}_m(K)$ for $m>2$. Moreover, we present a family of counter-examples to the statements of the First Fundamental Theorems for all finite fields and $m=2$.

math.AC↗