seminar announcement

[Emilia Mezzetti]

Seminar announcement
University of Trieste

Friday February 26, 2016, at 11 a.m.

Ada Boralevi (SISSA)

will speak on

How to obtain a space of matrices of constant rank by truncating 
graded modules.

Venue: Seminar Room  (DMG, Sezione di Matematica e Informatica, H2 
building, Via A.Valerio 12/1, 3rd floor, room 334)

Everybody interested is much welcome to attend.

Abstract: A space of matrices of constant rank is a vector subspace 
V, say of dimension n+1, of the set of matrices of size a x b over a 
field k, such that any nonzero element of V has fixed rank r. It is a 
classical problem to look for examples of such spaces of matrices, 
and to give relations among the possible values of the parameters 
a,b,r,n. In this talk I will report on a joint work with Daniele 
Faenzi and Paolo Lella, where we introduce a new effective method to 
construct explicit examples of such spaces.
I will show how linear matrices of relatively small size can be 
cooked up with two ingredients, namely two finitely generated graded 
modules E and G over the ring of polynomials k[x_0,...,x_n], 
admitting a linear resolution up to a certain step. The key idea here 
is that, in order for E to fit our purpose, it is necessary to 
truncate E above a certain range, typically its regularity, which 
ensures linearity of the resolution. To connect this result with 
linear matrices of constant rank, one takes E and G such that their 
sheafifications are vector bundles over P^n; this, together with one 
more technical assumption, guarantees that the presentation matrix of 
E, as well as that of any higher truncation of E, actually has 
constant rank.
In the last part of the talk I will focus on matrices with extra 
symmetry properties: I will show the conditions needed for a constant 
rank matrix constructed with our method to be skew-symmetrizable, 
connecting these new results with previous ones obtained with Daniele 
Faenzi and Emilia Mezzetti in [Linear spaces of matrices of constant 
rank and instanton bundles, Adv. in Math. 248 (2013)].


-- 
Prof. Emilia Mezzetti

Dipartimento di Matematica e Geoscienze
Sezione di Matematica e Informatica
Universita' di Trieste
Via Valerio 12/1
34127 Trieste, Italia

Stanza 227, II piano
e-mail: mezzette at units.it
tel. studio (+39) 040 558 2650
skype: emiliamezzetti
tel. Segreteria Dip.: (+39) 040 558 2635
fax: (+39) 040 558 2636
http://www.dmi.units.it/~mezzette/