Mathematics – Algebraic Geometry
Scientific paper
2002-12-16
Math. Res. Lett. 10 (2003), 219-236.
Mathematics
Algebraic Geometry
16 pages, AMS-LaTeX; v2: corrected reference; v3: last application, to the complete intersection of type (2,6) in P^8, was rem
Scientific paper
We use intersection theory, degeneration techniques and jet schemes to study log canonical thresholds. Our first result gives a lower bound for the log canonical threshold of a pair in terms of the log canonical threshold of the image by a suitable smooth morphism. This in turn is based on an inequality relating the log canonical threshold and the Samuel multiplicity, generalizing our previous result from math.AG/0205171. We then give a lower bound for the log canonical threshold of an affine scheme defined by homogeneous equations of the same degree in terms of the dimension of the non log terminal locus (this part supersedes math.AG/0105113). As an application of our results, we prove the birational superrigidity of every smooth hypersurface of degree N in P^N, if 4\leq N\leq 12.
Ein Lawrence
Fernex Tommaso de
Mustata Mircea
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