Veronese transform and Castelnuovo Mumford regularity of modules

: Veronese rings, Segre embeddings, or more generally Segre Veronese embeddings are very important rings in algebraic geometry. In this paper we present an original, elementary way to compute the Hilbert Poincar´e series of these rings; as a consequence we compute their Castelnuovo Mumford regularity and also the highest graded Betti number. Moreover, using the Castelnuovo Mumford regularity of a Cohen Macaulay finitely generated graded module, we compute that of its Veronese transforms.

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[1] Barcanescu S, Manolache N. Betti numbers of Segre-Veronese singularities. Rev Roum Math Pure 1981, A. 26, 549-565.
[2] Brenti F, Welker V. The Veronese construction for formal power series and graded algebras. Adv Appl Math 2009, 42, 545-556.
[3] Bruns W, Herzog J. Cohen-Macaulay rings. Cambridge, UK: Cambridge University Press, 1998.
[4] Cox DA, Materov E. Regularity and Segre-Veronese embeddings. P Am Math Soc 2009, 137: 1883-1890.
[5] Eisenbud D. The Geometry of Syzygies. A Second Course in Commutative Algebra and Algebraic Geometry. New York, NY, USA: Springer, 2005.
[6] Katzman M. The Hilbert series of algebras of the Veronese type. Commun Algebra 2005, 33: 1141-1146.
[7] Morales M. Fonctions de Hilbert, genre g´eom´etrique dune singularit´e quasi-homog´ene Cohen-Macaulay. CR Acad Sci I-Math 1985, t.301, s´erie I No.14, 699-702.

ISSN: 1300-0098
Yayın Aralığı: Yılda 6 Sayı
Yayıncı: TÜBİTAK

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