As an editor I often encounter the symbol $g\_d^r$ as a noun. I tried googling but I only get papers where the symbol is used without a definition. Can someone supply a reference to a definition? Examples of usage: "Koszul cohomology groups of $g\_d^r$s on singular nodal curves"; "any other basepoint-free $g\_h^1$ [...] is composed with the given $g\_d^1$.



Meaning of $g_d^r$ in algebraic geometry
As I understand, a $g\_d^r$ is a linear system of dimeansion $r$ and degree $d$. Basically, these give you maps to $\mathbb{P}^r$ of degree $d$. The simplest example is of course hyperelliptic curves; these are the same as a $g^1\_2$.


The reference that I have for this is Harsthorne, Algebraic Geometry, p. 341.


