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Algebra Seminar - Homomorphisms of maximal Cohen-Macaulay modules over the cone of an elliptic curve - Bhargavi Parthasarathy (Syracuse University)

Wednesday, November 12, 2025 11:15 AM – 12:05 PM
  • Description
    Homomorphisms of maximal Cohen-Macaulay modules over the cone of an elliptic curve by Bhargavi Parthasarathy (Syracuse University) Abstract: Consider the ring \(R=k[[x,y,z]]/(f)\) where \(f=x^3+y^3+z^3\) with an algebraically closed field \(k\) and \(char(k)
    eq 3\). In a 2002 paper, Laza, Popescu and Pfister used Atiyah's classification of vector bundles over elliptic curves to obtain a description of the maximal Cohen-Macaulay modules (MCM) over \(R\). In particular, the matrix factorizations corresponding to rank one MCMs can be described using points in \(V(f)\). If \(M,\ N\) are rank one MCMs over \(R\), then so is \({m Hom}_R(M,N)\). In this talk, I will discuss how the elliptic group law on \(f\) can be used to obtain the point in \(V(f)\) that describes the matrix factorization corresponding to \({m Hom}_R(M,N)\).
  • Website
    https://events.uconn.edu/mathematics-department/event/1439312-algebra-seminar-homomorphisms-of-maximal
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