Multigraded Hilbert Functions and Toric Complete Intersection Codes

Mesut Şahin; Ivan Soprunov

doi:10.1016/j.jalgebra.2016.04.013

Multigraded Hilbert Functions and Toric Complete Intersection Codes

Mesut Şahin, Ivan Soprunov

Hacettepe University

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

Abstract

Let X be a complete n -dimensional simplicial toric variety with homogeneous coordinate ring S . We study the multigraded Hilbert function H _Y HY of reduced 0-dimensional subschemes Y in X . We provide explicit formulas and prove non-decreasing and stabilization properties of H _Y HY when Y is a 0-dimensional complete intersection in X . We apply our results to computing the dimension of some evaluation codes on 0-dimensional complete intersection in simplicial toric varieties.

Original language	American English
Journal	Journal of Algebra
Volume	459
DOIs	https://doi.org/10.1016/j.jalgebra.2016.04.013
State	Published - Aug 1 2016

Keywords

Evaluation codes; Toric varieties; Multigraded Hilbert function

Disciplines

Algebra
Mathematics

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10.1016/j.jalgebra.2016.04.013License: CC BY

http://www.sciencedirect.com/science/article/pii/S0021869316300631

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title = "Multigraded Hilbert Functions and Toric Complete Intersection Codes",

abstract = " Let X be a complete n -dimensional simplicial toric variety with homogeneous coordinate ring S . We study the multigraded Hilbert function H Y HY of reduced 0-dimensional subschemes Y in X . We provide explicit formulas and prove non-decreasing and stabilization properties of H Y HY when Y is a 0-dimensional complete intersection in X . We apply our results to computing the dimension of some evaluation codes on 0-dimensional complete intersection in simplicial toric varieties.",

keywords = "Evaluation codes; Toric varieties; Multigraded Hilbert function",

author = "Mesut {\c S}ahin and Ivan Soprunov",

note = "{\c S}ahin, M., Soprunov, I. (2016). Multigraded hilbert functions and toric complete intersection codes. Journal of Algebra, 459, 446-467. doi:http://dx.doi.org/10.1016/j.jalgebra.2016.04.013",

year = "2016",

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doi = "10.1016/j.jalgebra.2016.04.013",

language = "American English",

volume = "459",

journal = "Journal of Algebra",

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T1 - Multigraded Hilbert Functions and Toric Complete Intersection Codes

AU - Şahin, Mesut

AU - Soprunov, Ivan

N1 - Şahin, M., Soprunov, I. (2016). Multigraded hilbert functions and toric complete intersection codes. Journal of Algebra, 459, 446-467. doi:http://dx.doi.org/10.1016/j.jalgebra.2016.04.013

PY - 2016/8/1

Y1 - 2016/8/1

N2 - Let X be a complete n -dimensional simplicial toric variety with homogeneous coordinate ring S . We study the multigraded Hilbert function H Y HY of reduced 0-dimensional subschemes Y in X . We provide explicit formulas and prove non-decreasing and stabilization properties of H Y HY when Y is a 0-dimensional complete intersection in X . We apply our results to computing the dimension of some evaluation codes on 0-dimensional complete intersection in simplicial toric varieties.

AB - Let X be a complete n -dimensional simplicial toric variety with homogeneous coordinate ring S . We study the multigraded Hilbert function H Y HY of reduced 0-dimensional subschemes Y in X . We provide explicit formulas and prove non-decreasing and stabilization properties of H Y HY when Y is a 0-dimensional complete intersection in X . We apply our results to computing the dimension of some evaluation codes on 0-dimensional complete intersection in simplicial toric varieties.

KW - Evaluation codes; Toric varieties; Multigraded Hilbert function

UR - https://engagedscholarship.csuohio.edu/scimath_facpub/121

UR - http://www.sciencedirect.com/science/article/pii/S0021869316300631

U2 - 10.1016/j.jalgebra.2016.04.013

DO - 10.1016/j.jalgebra.2016.04.013

M3 - Article

VL - 459

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Multigraded Hilbert Functions and Toric Complete Intersection Codes

Abstract

Keywords

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