TITLE: Meaning of $g_d^r$ in algebraic geometry
QUESTION [5 upvotes]: 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 $g_d^1$.

REPLY [5 votes]: 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.