I'm trying to find the definition of $g^1_3$ in algebraic geometry Hartshorne's book, anyone who is used with this book could help me to find this definition?
Thanks
Remark: this extract is from page 345 from Hartshorne's book.
2026-04-26 14:45:22.1777214722
What is $g^1_3$?
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The text does define a $g^r_d$; it's on the middle of page 341. For the sake of completeness: we say $C$ has a $g^r_d$ if it has a linear system of dimension $r$ and degree $d$.
This is a very old notation that's still in common use, even outside Hartshorne's book.