SPEAKER: Dmitry Kerner, U. Toronto
TOPIC:  On local determinantal representations of hypersurfaces, aka
maximally Cohen Macaulay modules
DATE: Thursday, Dec 23, 2010
TIME: 12:30
PLACE: Amado 719
Let M be a square matrix whose entries are series in several variables. M
is considered up to multiplication by locally invertible matrices from
both sides.
In classical algebraic geometry such an object is called the local
determinantal representation of the corresponding hypersurface {det(M)=0}.
In commutative algebra such objects are called maximally Cohen Macaulay
modules. In local geometry they correspond to specific elements of the
local class group.
When the hypersurface singularity is of ADE type the classification
of such modules is finite. For higher singularities such modules have
moduli and the classification problem is wild.
I will present various points of view on these objects. Time permitting I
will formulate some recent results: various necessary and sufficient
criteria of decomposability of modules over the hypersurfaces.
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