Computeralgebra

Macaulay2 packages

  1. (with G. Staglianò) K3surfaces.m2 (Explicit equations of K3 surfaces), Documentation

  2. (with C. Bopp) RelativeCanonicalResolution.m2 (Computation of relative canonical resolution and Eagon-Northcott type complexes), Documentation

  3. (with F. Tanturri) ExtensionsAndTorsWithLimitedDegree.m2 (Computation of the homogeneous components of the graded modules Ext^i(M,N) and Tor^i(M,N) with a fixed degree limit), Documentation

Macaulay2 files

  1. FlexibilityOfGeneralMukaiFourfolds.m2 (ancillary file to "Flexibility of affine cones over Mukai fourfolds of genus g>=7")

  2. CalabiYauCompleteIntersection.m2 (ancillary file to "Movable cones of complete intersections of multidegree one on products of projective spaces")

  3. CalabiYauThreefold.m2 (ancillary file to "On the numerical dimension of Calabi-Yau 3-folds of Picard number 2")

  4. ConstructingEllipticK3Surfaces-supportingM2files.zip (ancillary files to "Unirational moduli spaces of some elliptic K3 surfaces")

  5. relativeCanonicalResolutionsAndK3Surfaces.m2 (ancillary file to "Moduli of lattice polarized K3 surfaces via relative canonical resolutions")

  6. K3OfGenus8WithManyEllipticCurves.m2 (ancillary file to "Brill-Noether general K3 surfaces with the maximal number of elliptic pencils of minimal degree")

  7. surface.m2, surface-char0.m2 (ancillary files to "New examples of rational Gushel-Mukai fourfolds")

  8. M2codeThesisHoff.m2, constructionOfTheOsculatingCone.m2 (Macaulay2 code for my thesis)

The webpage (click here) lists all experimental results concerning the shape of relative canonical resolutions done with the Macaulay2 package "RelativeCanonicalResolution.m2"

Pictures and Animations

The osculating cone to a tetragonal curve of genus 6

To a general tetragonal canonical curve C of genus 6, we can associate a trigonal curve as follows. There is a pencil of planes intersecting C in the given g^1_4. Four different points in a plane has six connection lines which intersect in three further points. These further intersection points sweep out a trigonal curve C'. The union of C and C' is the osculating cone to the Brill-Noether locus W^0_4(C) at the given point g^1_4 of W^1_4(C). We denote by S the surface consisting of the connection lines swept out by the pencil of planes. Here you can see a real picture of the surface S with a highlighted plane.

An animation of the surface S and a moving plane can be found here. The animation based on an example in "The osculating cone to special Brill-Noether loci".