Abstract
Let \({X\subset\mathbb P^{n+1}}\) be a smooth complex projective hypersurface. In this paper we show that, if the degree of X is large enough, then there exist global sections of the bundle of invariant jet differentials of order n on X, vanishing on an ample divisor. We also prove a logarithmic version, effective in low dimension, for the log-pair \({(\mathbb P^n,D)}\) , where D is a smooth irreducible divisor of high degree. Moreover, these result are sharp, i.e. one cannot have such jet differentials of order less than n.
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Diverio, S. Existence of global invariant jet differentials on projective hypersurfaces of high degree. Math. Ann. 344, 293–315 (2009). https://doi.org/10.1007/s00208-008-0306-4
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DOI: https://doi.org/10.1007/s00208-008-0306-4