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:
1. The variety is non-singular.
2. The variety is a surface.
3. The variety is locally a complete intersection that is regular in codimension 2.
If time permits, we will show that the conjecture holds when the variety has only isolated singularities, under certain hypotheses.
This is based on the following joint work of I. Biswas and N. Das: arXiv:2504.18488.
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:
1. The variety is non-singular.
2. The variety is a surface.
3. The variety is locally a complete intersection that is regular in codimension 2.
If time permits, we will show that the conjecture holds when the variety has only isolated singularities, under certain hypotheses.
This is based on the following joint work of I. Biswas and N. Das: arXiv:2504.18488.