APS
Speaker: Manish Prasad, IIT Bombay
Host: Prachi Mahajan
Title: Castelnuovo Mumford Regularity Theorem.
Time, day and date: 4:00:00 PM – 5:00:00 PM, Wednesday, September 23
Venue: Room 105
Abstract: The m-regularity of a coherent sheaf on P^n is an important tool for the construction of the Quot scheme. In this presentation we will prove the Castelnuovo-Mumford regularity theorem, which allows us to conclude the m-regularity of some special coherent sheaves.
More precisely, we will prove the following:
Given any non-negative integers p, n, we show that there exists a polynomial F_p,n with integral coefficients such that for any coherent subsheaf G of p copies of the structure sheaf on P^n, G is F_p,n(a_0, a_1, a_2, ..., a_n)-regular, for suitable integers a_0, a_1, ..., a_n.