Mathematics Seminar
Date: Wednesday, 12 March 2025
Time: 2:00 - 3:00 PM
Venue: Seminar Hall
On Butler's Conjecture and some related results
Suhas B N
Chennai Mathematical Institute.
12-03-25

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Abstract

Let X be a smooth projective curve over the field of complex numbers. Let E be a semistable vector bundle on X of rank r which is globally generated by a subspace V of its sections of dimension at least r+1. We call such a pair (E,V) a generated pair on X. Given a generated pair (E,V) on X, one natural gets a vector bundle M_{E,V} associated to the this generated pair called the kernel bundle. With this setting, D C Butler conjectured that if X is a smooth curve of genus at least 3, and (E,V) is a generated pair on X, where E is a semistable vector bundle on X, then M_{E,V} is semistable.

In this talk, we first discuss the relevance of this conjecture in higher rank Brill-Noether theory. We then discuss the status of this conjecture at present. Finally, we discuss some related results when the base curve X is a certain type of reducible nodal curve. This last part is joint work with Praveen Kumar Roy and Amit Kumar Singh.