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Frobenius stable pluricanonical systems on threefolds of general type in positive characteristic

Lei Zhang

Vol. 16 (2022), No. 10, 2339–2384

This paper investigates effectivity problems of pluricanonical systems on varieties of general type in positive characteristic. In practice, we will consider a sublinear system |S0(X,KX + nKX)||H0(X,KX + nKX)| generated by certain Frobenius stable sections, and prove that for a minimal terminal threefold X of general type with either q(X) > 0 or Gorenstein singularities, if n 28 then |S0(X,KX + nKX)|; and if n 42 then the linear system |S0(X,KX + nKX)| defines a birational map.

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effectivity problems, pluricanonical systems, positive characteristic, Frobenius stable sections
Mathematical Subject Classification
Primary: 14E05, 14E30
Received: 27 February 2021
Revised: 5 January 2022
Accepted: 18 February 2022
Published: 28 January 2023
Lei Zhang
School of Mathematical Science
University of Science and Technology of China