Title of Seminar: Algebraic Geometry Preprint Seminar 2025
Title of Talk: ON THE INJECTIVE SELF-MAPS OF ALGEBRAIC VARIETIES
Speaker: Parnashree Ghosh, TIFR, Mumbai
Date: September 23, 2025
Time: 16:00:00 Hours
Venue: AG-77

Abstract: A conjecture of Miyanishi says that an endomorphism of an algebraic variety, defined over an algebraically closed field of characteristic zero, is an automorphism if the endomorphism is injective outside a closed subset of codimension at least 2. We will see a proof of this conjecture in the following cases: <br> 1. The variety is non-singular. <br> 2. The variety is a surface. <br> 3. The variety is locally a complete intersection that is regular in codimension 2. <br> If time permits, we will show that the conjecture holds when the variety has only isolated singularities, under certain hypotheses. <br> This is based on the following joint work of I. Biswas and N. Das: arXiv:2504.18488.