Pure and Applied Mathematics Quarterly

Volume 18 (2022)

Number 1

Special Issue in Honor of Bernie Shiffman

Guest Editors: Yuan Yuan, Christopher Sogge, and Steven Morris Zelditch

Lines, conics, and all that

Pages: 101 – 176

DOI: https://dx.doi.org/10.4310/PAMQ.2022.v18.n1.a4


Ciro Ciliberto (Dipartimento di Matematica, Università degli Studi di Roma “Tor Vergata”, Italy)

Mikhail Zaidenberg (Institut Fourier, Laboratoire de Mathématiques, Université Grenoble Alpes, Grenoble, France)


This is a survey on the Fano schemes of linear spaces, conics, rational curves, and curves of higher genera in smooth projective hypersurfaces, complete intersections, Fano threefolds, on the related Abel–Jacobi mappings, etc.


line, conic, rational curve, Fano threefold, projective hypersurface, complete intersection, Fano scheme, Abel–Jacobi mapping

2010 Mathematics Subject Classification

Primary 14-02, 14H15, 14N10, 14Q10. Secondary 14N25.

The authors’ research was supported by the MIUR Excellence Department Project awarded to the Department of Mathematics, University of Rome Tor Vergata, CUP E83C18000100006.

Ciro Ciliberto is a member of GNSAGA of INdAM.

Received 19 February 2020

Accepted 23 March 2020

Published 10 February 2022