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Abstract
The sheaf of differential operators on log schemes is defined and studied. Then logarithmic differential operators on compactified Jacobians of singular curves are studied. In particular, a logarithmic heat equation for theta functions is produced geometrically.
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ACKNOWLEDGMENTS
This work was done during my stay at FB 6 Mathematik of Universitรคt Essen. I would like to express my hearty thanks to Prof. H. Esnault and Prof. E. Viehweg for their hospitality and encouragement. I have benefited from stimulating discussions with them, which helped to prove Lemma 3.3 and Definition 1.3. Discussions with H. Clemens, I-Hsun Tsai, and Kang Zuo, and the emails of Z. Ran, were very helpful. I thank them very much.