Determinantal representation and subschemes of general plane curves

Details Determinantal representation and subschemes of general plane curves Determinantal representation and subschemes of general plane curves

2010-12-15

arxiv.org/abs/1012.3396v1

Mathematics

Algebraic Geometry

14 pages

Scientific paper

Let $M = (m_{ij})$ be an $n \times n$ square matrix of integers. For our purposes, we can assume without loss of generality that $M$ is homogeneous and that the entries are non-increasing going leftward and downward. Let $d$ be the sum of the entries on either diagonal. We give a complete characterization of which such matrices have the property that a general form of degree $d$ in $\mathbb C[x_0,x_1,x_2]$ can be written as the determinant of a matrix of forms $(f_{ij})$ with $\deg f_{ij} = m_{ij}$ (of course $f_{ij} = 0$ if $m_{ij} < 0$). As a consequence, we answer the related question of which $(n-1) \times n$ matrices $Q$ of integers have the property that a general plane curve of degree $d$ contains a zero-dimensional subscheme whose degree Hilbert-Burch matrix is $Q$. This leads to an algorithmic method to determine properties of linear series contained in general plane curves.

Affiliated with

Also associated with

No associations

Rating

Determinantal representation and subschemes of general plane curves does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Determinantal representation and subschemes of general plane curves, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Determinantal representation and subschemes of general plane curves will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-14338