The minimal resolution conjecture on a general quartic surface in P3

M. Boij; J. Migliore; R. M. Miró-Roig; U. Nagel

doi:10.1016/j.jpaa.2018.06.014

The minimal resolution conjecture on a general quartic surface in P³

M. Boij, J. Migliore, R. M. Miró-Roig, U. Nagel

Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	1456-1471
Number of pages	16
Journal	Journal of Pure and Applied Algebra
Volume	223
Issue number	4
DOIs	https://doi.org/10.1016/j.jpaa.2018.06.014
State	Published - Apr 2019

Bibliographical note

Funding Information:
Acknowledgements: Boij was partially supported by the grant VR2013-4545. Migliore was partially supported by Simons Foundation grant # 309556 . Miró-Roig was partially supported by MTM2016-78623-P. Nagel was partially supported by Simons Foundation grant # 317096 . This paper resulted from work done during a Research in Pairs stay at the Mathematisches Forschungsinstitut Oberwolfach in 2017. All four authors are grateful for the stimulating atmosphere and the generous support of the MFO , as well as to the referee for insightful comments.

Publisher Copyright:
© 2018 Elsevier B.V.

ASJC Scopus subject areas

Algebra and Number Theory

Access to Document

10.1016/j.jpaa.2018.06.014

Cite this

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title = "The minimal resolution conjecture on a general quartic surface in P3 ",

abstract = "Musta{\c t}{\u a} 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.",

author = "M. Boij and J. Migliore and Mir{\'o}-Roig, {R. M.} and U. Nagel",

note = "Funding Information: Acknowledgements: Boij was partially supported by the grant VR2013-4545. Migliore was partially supported by Simons Foundation grant # 309556 . Mir{\'o}-Roig was partially supported by MTM2016-78623-P. Nagel was partially supported by Simons Foundation grant # 317096 . This paper resulted from work done during a Research in Pairs stay at the Mathematisches Forschungsinstitut Oberwolfach in 2017. All four authors are grateful for the stimulating atmosphere and the generous support of the MFO , as well as to the referee for insightful comments. Publisher Copyright: {\textcopyright} 2018 Elsevier B.V.",

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