RandomGenus14Curves -- Construction of random curves of genus 14

Description

In this package the unirationality construction of the moduli space $M_{14}$ of curves of genus 14 due to Verra is implemented. The main references are

\ \ \ \ \ [Mu] S. Mukai, Curves, $K3$ surfaces and Fano $3$-folds of genus $\leq 10$. Algebraic geometry and commutative algebra, Vol. I, 357-377, Kinokuniya, Tokyo, 1988.

\ \ \ \ \ [Ve] A. Verra, The unirationality of the moduli spaces of curves of genus 14 or lower. Compos. Math. 141 (2005), no. 6, 1425-1444.

Authors

Version

This documentation describes version 0.6 of RandomGenus14Curves.

Citation

If you have used this package in your research, please cite it as follows:

@misc{RandomGenus14CurvesSource,
  title = {{RandomGenus14Curves: random smooth curves of genus 14. Version~0.6}},
  author = {Frank-Olaf Schreyer and Hans-Christian Graf v. Bothmer},
  howpublished = {A \emph{Macaulay2} package available at
    \url{https://github.com/Macaulay2/M2/tree/master/M2/Macaulay2/packages}}
}

Exports

Functions and commands
- randomCanonicalCurveGenus8with8Points -- Compute a random canonical curve of genus 8 with 8 marked point
- randomCurveGenus8Degree14inP6 -- Compute a random normal curve of genus g=8 and degree 14 in \PP^6
- randomCurveGenus14Degree18inP6 -- Compute a random curve of genus 14 of Degree 18 in \PP^6
Methods
- randomCanonicalCurveGenus8with8Points(PolynomialRing) -- see randomCanonicalCurveGenus8with8Points -- Compute a random canonical curve of genus 8 with 8 marked point
- randomCurveGenus8Degree14inP6(PolynomialRing) -- see randomCurveGenus8Degree14inP6 -- Compute a random normal curve of genus g=8 and degree 14 in \PP^6
- randomCurveGenus14Degree18inP6(PolynomialRing) -- see randomCurveGenus14Degree18inP6 -- Compute a random curve of genus 14 of Degree 18 in \PP^6
Other things
- canonicalCurveGenus14 -- compute a random curve of genus 14 in its canonical embedding
- curveGenus14Degree18inP6 -- compute a random curve of genus 14 and degree 18 in $\mathbb{P}^6$

For the programmer

The object RandomGenus14Curves is a package, defined in RandomGenus14Curves.m2.

The source of this document is in RandomGenus14Curves.m2:180:0.