Department of Mathematics

Student Algebra & Combinatorics

  •  Nick Rekuski, MSU
  •  Minimal Free Resolutions
  •  04/01/2019
  •  3:00 PM - 4:00 PM
  •  C517 Wells Hall

The Hilbert function is a classical invariant of a variety (with a given embedding) that is easy to compute. It determines some properties of the variety (such as degree, dimension, and arithmetic genus), but it cannot determine more sophisticated invariants. A minimal free resolution determines more sophisticated properties of the variety while still being easily computable. For example, any set of seven points in P^3 in linearly general position has the same Hilbert function, but minimal free resolutions can distinguish whether the points lie on a rational normal curve. Furthermore, a minimal free resolution retains all the information of the Hilbert function. In this talk, we will define a minimal free resolution and associated invariants. With the definitions in place, we will show that minimal free resolutions retain all the information of the Hilbert function then explain the above example. If time permits, we will additionally show that minimal free resolutions are well behaved when restricting a variety to a hypersurface.

 

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Department of Mathematics
Michigan State University
619 Red Cedar Road
C212 Wells Hall
East Lansing, MI 48824

Phone: (517) 353-0844
Fax: (517) 432-1562

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