A <math>g_rg^dr_d</math> is a linear system <math> \mathfrak{d} </math> on a curve <math>C</math> which is of degree <math>d</math> and dimension <math>r</math>. For example, hyperelliptic curves have a <math>g^1_2</math> since <math>|K_C|</math> defines one. In fact, hyperelliptic curves have a unique <math>g^1_2</math><ref name=":0" /> from proposition 5.3. Another close set of examples are curves with a <math>g_1^3</math> which are called [[Trigonal curve|trigonal curves]]. In fact, any curve has a <math>g^d_1</math> for <math>d \geq (1/2)g + 1</math>.<ref>{{Cite journal|last1=Kleiman|first1=Steven L.|last2=Laksov|first2=Dan|date=1974|title=Another proof of the existence of special divisors|url=https://projecteuclid.org/euclid.acta/1485889804|journal=Acta Mathematica|language=EN|volume=132|pages=163–176|doi=10.1007/BF02392112|issn=0001-5962|doi-access=free}}</ref>
===Linear systems of hypersurfaces in a projective space===
