The minimal resolution conjecture on a general quartic surface in P3

Mustaţă has given a conjecture for the graded Betti numbers in the minimal free resolution of the ideal of a general set of points on an irreducible projective algebraic variety. For surfaces in P3 this conjecture has been proven for points on quadric surfaces and on general cubic surfaces. In the latter case, Gorenstein liaison was the main tool. Here we prove the conjecture for general quartic surfaces. Gorenstein liaison continues to be a central tool, but to prove the existence of our links we make use of certain dimension computations. We also discuss the higher degree case, but now the dimension count does not force the existence of our links.

Keywords

Minimal resolution conjecture, Mustaţă conjecture, Betti numbers, Gorenstein ideals, liaison, linkage, Hilbert scheme

URI

https://doi.org/10.34657/3375
https://oa.tib.eu/renate/handle/123456789/2609

Citation

Boij, M., Migliore, J., Miró-Roig, R. M., & Nagel, U. (2017). The minimal resolution conjecture on a general quartic surface in P3 (Vol. 2017-21). Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach. https://doi.org//10.14760/OWP-2017-21

Collections

Mathematik
Oberwolfach Preprints (OWP)

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