Uniform bounds on multigraded regularity
By Diane Maclagan, Gregory G. Smith. 2003
71 citations recorded by the source corpus.
We give an effective uniform bound on the multigraded regularity of a subscheme of a smooth projective toric variety X with a given multigraded Hilbert polynomial. To establish this bound, we introduce a new combinatorial tool, called a Stanley filtration, for studying monomial ideals in the homogeneous coordinate ring of X. As a special case, we obtain a new proof of Gotzmann’s regularity theorem. We also discuss applications of this bound to the construction of multigraded Hilbert
Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/aaaae5d983cc6dc597cc2f3165ad7e7eba9d1508
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In Algebra and Number Theory
- Ali Soleyman Jahan
- Jürgen Herzog
- Gregory G. Smith
- Diane Maclagan
- Dorin Vicentiu Popescu
- Asia Rauf
- Takayuki Hibi
- H. Iritani
In Computational Theory and Mathematics
- Ali Soleyman Jahan
- Jürgen Herzog
- Gregory G. Smith
- Diane Maclagan
- Dorin Vicentiu Popescu
- Asia Rauf
- Huy Tài Hà
- Takayuki Hibi
In Geometry and Topology
- Ali Soleyman Jahan
- Jürgen Herzog
- Gregory G. Smith
- Diane Maclagan
- Dorin Vicentiu Popescu
- Asia Rauf
- H. Iritani
- Huy Tài Hà
Citations in the corpus
- Prime filtrations of monomial ideals and polarizations (2006, methodology): “Such an example is given by McLagan and Smith in [7].”
- Multigraded Castelnuovo-Mumford Regularity (2003, background): “Example 2.16 in [ MS ] rephrases the following result in terms of the associated multigraded Hilbert polynomial.”
- Finite filtrations of modules and shellable multicomplexes (2005, background): “Stanley decompositions have been studied in various combinatorial and algebraic contexts, see [1], [8], and [9].”