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SUMMARY:Mesut Şahin (Hacettepe)
DTSTART:20230428T120000Z
DTEND:20230428T130000Z
DTSTAMP:20260423T021257Z
UID:OBAGS/26
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OBAGS/26/">V
 anishing ideals and codes on toric varieties</a>\nby Mesut Şahin (Hacette
 pe) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstract\nMot
 ivated by applications to the theory of error-correcting codes\, we give a
 n algorithmic method for computing a generating set for the ideal generate
 d by $\\beta$-graded polynomials vanishing on a subset of a simplicial com
 plete toric variety $X$ over a finite field $\\mathbb{F}_q$\, parameterize
 d by rational functions\, where $\\beta$ is a $d\\times r$ matrix whose co
 lumns generate a subsemigroup $\\mathbb{N}\\beta$ of $\\mathbb{N}^d$. We a
 lso give a method for computing the vanishing ideal of the set of $\\mathb
 b{F}_q$-rational points of $X$. We talk about some of its algebraic invari
 ants related to basic parameters of the corresponding evaluation code. Whe
 n $\\beta=[w_1 \\cdots w_r]$ is a row matrix corresponding to a numerical 
 semigroup $\\mathbb{N}\\beta=\\langle w_1\,\\dots\,w_r \\rangle$\, $X$ is 
 a weighted projective space and generators of its vanishing ideal is relat
 ed to the generators of the defining (toric) ideals of some numerical semi
 group rings corresponding to semigroups generated by subsets of $\\{w_1\,\
 \dots\,w_r\\}$.\n
LOCATION:https://researchseminars.org/talk/OBAGS/26/
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