Weak boundedness of Fano threefolds with large Seshadri constants in characteristic $p>5$

Abstract

Given $\epsilon>0$, we show that over an algebraically closed field of characteristic $p>5$, the anticanonical volume of a Fano threefold $X$ (with arbitrary singularities) whose anticanonical divisor has Seshadri constant $\epsilon(-K_X,x)>2+\epsilon$ at some smooth point $x\in X$ is bounded from above.