The minimal resolution conjecture on a general quartic surface in P3 |
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| Authors: | M. Boij J. Migliore R.M. Miró-Roig U. Nagel |
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| Affiliation: | 1. Department of Mathematics, KTH Royal Institute of Technology, S-100 44 Stockholm, Sweden;2. Department of Mathematics, University of Notre Dame, Notre Dame, IN 46556, USA;3. Facultat de Matemàtiques, Departament de Matemàtiques i Informàtica, Gran Via des les Corts Catalanes 585, 08007 Barcelona, Spain;4. Department of Mathematics, University of Kentucky, 715 Patterson Office Tower, Lexington, KY 40506-0027, USA |
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| Abstract: | Musta?? 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 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. |
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| Keywords: | 13D02 13C40 13D40 13E10 14M06 |
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