Jet Schemes and Singularities of W d ( C ) Loci.

Kempf proved that the theta divisor of a smooth projective curveChas rational singularities. In this paper we estimate the dimensions of the jet schemes of the theta divisor and show that all these schemes are irreducible. In particular, we recover Kempf's theorem in this way. For general projective smooth curves, our method also gives a formula for the log canonical threshold of the pair. [ABSTRACT FROM PUBLISHER]