## Abstract

We study elementary transformations, first introduced by Livsic and Kravitsky in an operator-theoretic context, of determinantal representations of algebraic curves. We consider determinantal representations of a smooth irreducible curve F over an algebraically closed field. When regarded as acting on the corresponding vector bundle the elementary transformations are a matrix generalization of scalar linear fractional transformations: they add to the class of divisors of the vector bundle a single zero and a single pole. We show that given a determinantal representation of F, we can build all the nonequivalent determinantal representations of F by applying to the given representation finite sequences of at most g elementary transformations, where g is the genus of F.

Original language | English |
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Pages (from-to) | 1-18 |

Number of pages | 18 |

Journal | Linear Algebra and Its Applications |

Volume | 135 |

Issue number | C |

DOIs | |

State | Published - 1 Jan 1990 |

## ASJC Scopus subject areas

- Algebra and Number Theory
- Numerical Analysis
- Geometry and Topology
- Discrete Mathematics and Combinatorics