CMI PhD Research Seminar
Date: Monday, 21 October 2024
Time: 04:00 - 05:00 PM
Venue: Seminar Hall
Strength and Hartshorne’s conjecture in high degree
Abhiram Subramanian
Chennai Mathematical Institute.
21-10-24

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Abstract

In 1970s, Hartshorne conjectured that nonsingular, irreducible varieties (over algebraically closed fields) of codimension $c$ in $P^n$, with $c < n/3$, must be complete intersections. In the same paper, Hartshorne proved the conjecture for varieties $X$ over $C$ such that $n >> \deg X$. In this seminar, we take a look at Erman-Sam-Snowden’s paper titled “Strength and Hartshorne’s conjecture in high degree”, where the authors prove Hartshorne’s conjecture for non-degenerate varieties of high degree. In particular, we touch upon the concepts of strength and ultraproducts, which are used in the proof.