One key divisor on a compact Riemann surface is the canonical divisor. To define it, one first defines the divisor of a nonzero meromorphic 1-form along the lines above. Since the space of meromorphic 1-forms is a 1-dimensional vector space over the field of meromorphic functions, any two nonzero meromorphic 1-forms yield linearly equivalent divisors. Any divisor in this linear equivalence class is called the canonical divisor of "X", "K""X". The genus "g" of "X" can be read from the canonical divisor: namely, "K""X" has degree 2"g" − 2. The key trichotomy among compact Riemann surfaces "X" is whether the canonical divisor has negative degree (so "X" has genus zero), zero degree (genus one), or positive degree (genus at least 2). For example, this determines whether "X" has a Kähler metric with positive curvature, zero curvature, or negative curvature. The canonical divisor has negative degree if and only if "X" is isomorphic to the Riemann sphere CP1.