## Tangent developable surfaces and the equations defining algebraic curves

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Lawrence Ein and Robert Lazarsfeld
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## Abstract:

This is an introduction, aimed at a general mathematical audience, to recent work of Aprodu, Farkas, Papadima, Raicu, and Weyman. These authors established a long-standing folk conjecture concerning the equations defining the tangent developable surface of the rational normal curve. This in turn led to a new proof of a fundamental theorem of Voisin on the syzygies of generic canonical curves. The present note, which is the write-up of a talk given by the second author at the Current Events seminar at the 2019 JMM, surveys this circle of ideas.## References

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## Additional Information

**Lawrence Ein**- Affiliation: Department of Mathematics, University of Illinois at Chicago, 851 South Morgan St., Chicago, Illinois 60607
- MR Author ID: 62255
- Email: ein@uic.edu
**Robert Lazarsfeld**- Affiliation: Department of Mathematics, Stony Brook University, Stony Brook, New York 11794
- MR Author ID: 111255
- Email: robert.lazarsfeld@stonybrook.edu
- Received by editor(s): June 12, 2019
- Published electronically: October 15, 2019
- Additional Notes: The research of the first author was partially supported by NSF grant DMS-1801870

The research of the second author was partially supported by NSF grant DMS-1739285 - © Copyright 2019 American Mathematical Society
- Journal: Bull. Amer. Math. Soc.
**57**(2020), 23-38 - MSC (2010): Primary 14H99, 13D02
- DOI: https://doi.org/10.1090/bull/1683
- MathSciNet review: 4037406