Michael Hoff

ehem. Hahn


Room: 428

Phone: +49681/302-3227

Email: This email address is being protected from spambots. You need JavaScript enabled to view it.

Research Interests:

  • osculating cones to Brill-Noether loci,   
  • local structure of the moduli space of vector bundles,
  • experimental methods of computer algebra in algebraic geometry,
  • (relative) canonical resolutions of curves,
  • K3 surfaces and Fano manifolds.




Pictures and Animations:

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.                         connectionLinesMovingPlane600

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".


RelativeCanonicalResolution.m2 Documentation Computation of relative canonical resolution and Eagon-Northcott type complexes
ExtensionsAndTorsWithLimitedDegree.m2 Documentation Computation of the homogeneous components of the graded modules Ext^i(M,N) and Tor^i(M,N) with a fixed degree limit 
M2codeThesisHoff.m2 / constructionOfTheOsculatingCone.m2   M2 code for my thesis
relativeCanonicalResolutionsAndK3Surfaces.m2   ancillary file to "Moduli of lattice polarized K3 surfaces via relative canonical resolutions" 
surface.m2, surface-char0.m2   ancillary files to "New examples of rational Gushel-Mukai fourfolds"


  ancillary file to "Brill-Noether general K3 surfaces with the maximal number of elliptic pencils of minimal degree"
 ConstructingEllipticK3Surfaces-supportingM2files.zip    ancillary files to "Unirational moduli spaces of some elliptic K3 surfaces"

Experiments concerning relative canonical resolutions:

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


  • 03/2017 - present: Postdoc at the Universität des Saarlandes
  • 09/2012 - 03/2017: Ph.D. student at the Universität des Saarlandes
  • 09/2012 - 03/2013: DAAD study visit at the University of Oslo, Norway
  • 04/2012 - 08/2012: M. Sc. in Mathematics at the Universität des Saarlandes
  • 04/2008 - 03/2012: B. Sc. in Mathematics at the Universität des Saarlandes
© AG Schreyer