VSPs of cubic fourfolds and the Gorenstein locus of the Hilbert
... Example 10. Take A = k[t] and F = tx ∈ A[x]. Then Ann (F ) = (α2 ), so that the fibers of the associated apolar family are all equal to k[α]/α2 . For t = λ non-zero we have k[α]/α2 = Apolar (Fλ ), but for t = 0 we have F0 = 0, so the fiber is not the apolar algebra of F0 . Intuitively, we think of Apo ...
... Example 10. Take A = k[t] and F = tx ∈ A[x]. Then Ann (F ) = (α2 ), so that the fibers of the associated apolar family are all equal to k[α]/α2 . For t = λ non-zero we have k[α]/α2 = Apolar (Fλ ), but for t = 0 we have F0 = 0, so the fiber is not the apolar algebra of F0 . Intuitively, we think of Apo ...
On the structure of triangulated categories with finitely many
... obtain the same result with a new proof in section 4, namely that each connected component of the Auslander-Reiten quiver of the category T is of the form Z∆/G, where ∆ is a simply laced Dynkin diagram and G is trivial or a weakly admissible group of automorphisms. We are interested in the k-linear ...
... obtain the same result with a new proof in section 4, namely that each connected component of the Auslander-Reiten quiver of the category T is of the form Z∆/G, where ∆ is a simply laced Dynkin diagram and G is trivial or a weakly admissible group of automorphisms. We are interested in the k-linear ...
Equivalence Relations
... Equivalence relations The concept of equivalence relation is an abstraction of the idea of two math objects being like each other in some respect. If an object a is like an object b in some specified way, then b is like a in that respect. a is like itself in every respect! So if you want to give ...
... Equivalence relations The concept of equivalence relation is an abstraction of the idea of two math objects being like each other in some respect. If an object a is like an object b in some specified way, then b is like a in that respect. a is like itself in every respect! So if you want to give ...
Not For Sale
... A set is a collection of objects, such as a set of dishes or a set of golf clubs. The set of vowels in the English language can be denoted as 5 a, e, i, o, u 6 , where the braces 5 6 are read as “the set of.” If every member of one set B is also a member of another set A, we say that B is a subset o ...
... A set is a collection of objects, such as a set of dishes or a set of golf clubs. The set of vowels in the English language can be denoted as 5 a, e, i, o, u 6 , where the braces 5 6 are read as “the set of.” If every member of one set B is also a member of another set A, we say that B is a subset o ...
Character Tables of Metacyclic Groups
... Unless stated otherwise, all groups considered will be finite. If H is a subgroup of G and V is a representation of G, then we can obtain a restricted representation by considering V as a CH module. Alternately, if V is a representation of H then V ⊗CH CG is a representation of G, called the induced ...
... Unless stated otherwise, all groups considered will be finite. If H is a subgroup of G and V is a representation of G, then we can obtain a restricted representation by considering V as a CH module. Alternately, if V is a representation of H then V ⊗CH CG is a representation of G, called the induced ...
