Abstrakt:
Given a complex vector space V of dimension n,

one can look at d-dimensional linear subspaces A in

Alt^2(V), whose elements have constant rank r. The

natural interpretation of A as a vector bundle map

yields some restrictions on the values that r, n and d

can attain. After a brief overview of the subject and

of the main techniques used, I will concentrate on the

case r=n-2 and d=4. I will introduce what used to be the

only known example, by Westwick, and give an explanation

of this example in terms of instanton bundles and the

derived category of P^3. I will then present a new

method that allows one to prove the existence of new

examples of such spaces, and show how this method

applies to instanton bundles of charge 2 and 4.

These results are in collaboration with D.Faenzi and

E.Mezzetti.

one can look at d-dimensional linear subspaces A in

Alt^2(V), whose elements have constant rank r. The

natural interpretation of A as a vector bundle map

yields some restrictions on the values that r, n and d

can attain. After a brief overview of the subject and

of the main techniques used, I will concentrate on the

case r=n-2 and d=4. I will introduce what used to be the

only known example, by Westwick, and give an explanation

of this example in terms of instanton bundles and the

derived category of P^3. I will then present a new

method that allows one to prove the existence of new

examples of such spaces, and show how this method

applies to instanton bundles of charge 2 and 4.

These results are in collaboration with D.Faenzi and

E.Mezzetti.