Kawamata-Miyaoka-type inequality for $\mathbb{Q}$-Fano varieties with canonical singularities II: Terminal $\mathbb{Q}$-Fano threefolds

Abstract

We prove an optimal Kawamata-Miyaoka-type inequality for terminal $\mathbb{Q}$-Fano threefolds with Fano index at least $3$. As an application, any terminal $\mathbb{Q}$-Fano threefold $X$ satisfies the following Kawamata-Miyaoka-type inequality \[ c_1(X)^3 < 3c_2(X)c_1(X). \]

33 pages, 4 tables. Any comments are welcome. v2: we improve the exposition, 29 pages, 3 tables. v3: Final published vesion

References in corpus (2)

• Miyaoka type inequality for terminal threefolds with nef anti-canonical divisors
• On the birational geometry of $\mathbf{Q}$-Fano threefolds of large Fano index, I