Noetherianity for infinite-dimensional toric varieties
| Autor: | Rob H. Eggermont, Anton Leykin, Jan Draisma, Robert Krone |
|---|---|
| Přispěvatelé: | Discrete Algebra and Geometry, Mathematics |
| Jazyk: | angličtina |
| Rok vydání: | 2015 |
| Předmět: |
Monoid
Discrete mathematics Pure mathematics Monomial Algebra and Number Theory 13E05 13E15 13P10 Mathematics::Commutative Algebra Noetherianity up to symmetry Syntactic monoid 13E05 Monoid ring Mathematics - Commutative Algebra Commutative Algebra (math.AC) binomial ideals Kernel (algebra) Free monoid FOS: Mathematics Equivariant map 13P10 14M25 Mathematics Trace theory |
| Zdroj: | Draisma, J, Eggermont, R H, Krone, R & Leykin, A 2015, ' Noetherianity for infinite-dimensional toric varieties ', Algebra & Number Theory, vol. 9, no. 8, pp. 1857-1880 . https://doi.org/10.2140/ant.2015.9.1857 Algebra & Number Theory, 9(8), 1857-1880. Mathematical Sciences Publishers Algebra Number Theory 9, no. 8 (2015), 1857-1880 |
| ISSN: | 1944-7833 1937-0652 |
| Popis: | We consider a large class of monomial maps respecting an action of the infinite symmetric group, and prove that the toric ideals arising as their kernels are finitely generated up to symmetry. Our class includes many important examples where Noetherianity was recently proved or conjectured. In particular, our results imply Hillar-Sullivant's Independent Set Theorem and settle several finiteness conjectures due to Aschenbrenner, Martin del Campo, Hillar, and Sullivant. We introduce a matching monoid and show that its monoid ring is Noetherian up to symmetry. Our approach is then to factorize a more general equivariant monomial map into two parts going through this monoid. The kernels of both parts are finitely generated up to symmetry: recent work by Yamaguchi-Ogawa-Takemura on the (generalized) Birkhoff model provides an explicit degree bound for the kernel of the first part, while for the second part the finiteness follows from the Noetherianity of the matching monoid ring. Comment: 20 pages |
| Databáze: | OpenAIRE |
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