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Curves on complete intersections and measures of irrationality

SEMINARS: HARVARD-MIT ALGEBRAIC GEOMETRY

When: September 17, 2024
3:00 pm - 4:00 pm
Where: Science Center 507
Address: 1 Oxford Street, Cambridge, MA 02138, United States
Speaker: Benjamin Church (Stanford University)

Given a projective variety $X$, it is always covered by curves obtained by taking the intersection with a linear subspace. We study whether there exist curves on $X$ that have smaller numerical invariants than those of the linear slices. If $X$ is a general complete intersection of large degrees, we show that there are no curves on $X$ of smaller degree, nor are there curves of asymptotically smaller gonality. This verifies a folklore conjecture on the degrees of subvarieties of complete intersections as well as a conjecture of Bastianelli–De Poi–Ein–Lazarsfeld–Ullery on measures of irrationality for complete intersections. This is joint work with Nathan Chen and Junyan Zhao.

For more information, please see https://researchseminars.org/seminar/harvard-mit-ag-seminar