標(biāo)題: Titlebook: Determinants, Gr?bner Bases and Cohomology; Winfried Bruns,Aldo Conca,Matteo Varbaro Book 2022 Springer Nature Switzerland AG 2022 Determi [打印本頁] 作者: 動詞 時間: 2025-3-21 18:13
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作者: Abbreviate 時間: 2025-3-21 20:38
Algebras Defined by Minors,rated by minors through their initial algebras. Since the initial algebras are normal monoid domains, toric algebra can be applied to them. Since normal monoid domains are very well understood, we can draw strong consequences for the algebras defined by minors.作者: reflection 時間: 2025-3-22 04:17
-singularities of Determinantal Rings,lop them far enough to prove that determinantal rings are strongly F-regular. For deformation arguments one needs F-rationality. It is closely related to the rationality of singularities in characteristic 0, so that we can at least briefly discuss this property for determinantal rings. F-rationality作者: 痛得哭了 時間: 2025-3-22 05:22
,Castelnuovo–Mumford Regularity,ratch, but in a more general version for standard graded algebras over Noetherian base rings. As in the classical case, regularity can be computed from local cohomology, minimal free resolutions and Koszul homology. In the given generality we prove the theorems on the regularity of powers and produc作者: Ostrich 時間: 2025-3-22 09:05
Grassmannians, Flag Varieties, Schur Functors and Cohomology,hasis on vanishing statements. We develop the theory in the relative setting, which offers significant flexibility for the inductive arguments that we employ. We also introduce Schur functors and explain their relationship to direct images of line bundles associated to dominant weights. We end with 作者: 最后一個 時間: 2025-3-22 16:52 作者: 最后一個 時間: 2025-3-22 18:02 作者: 吞吞吐吐 時間: 2025-3-22 23:14 作者: 獨特性 時間: 2025-3-23 03:05
https://doi.org/10.1007/978-3-319-77568-5The second chapter pushes the discussion of the Gr?bner deformation forward in several directions: finer control of minimal and associated primes, connectedness, tight connections between an ideal and its squarefree initial ideals, should the latter exist. Some of these results were very recently established by Conca and Varbaro.作者: 悲痛 時間: 2025-3-23 07:18
Generations of Women HistoriansIn this chapter gives a short introduction to standard bitableaux and the straightening law. This powerful technique is the key to structural properties of determinantal rings. But it is also of central importance for the computation of Gr?bner and Sagbi bases on the one hand and for the representation theoretic approach on the other.作者: 一條卷發(fā) 時間: 2025-3-23 13:15
Generations of Women HistoriansChapter 5 covers the existence of universal Gr?bner bases of determinantal ideals as far as they are known, namely maximal minors and 2-minors. The approach to the case of maximal minors is particularly simple.作者: 不可思議 時間: 2025-3-23 17:44
,Gr?bner Bases, Initial Ideals and Initial Algebras,The first chapter gives a compact, but quite complete introduction to Gr?bner bases and Sagbi bases in general. The focus is on the structural aspects, namely, the use of Gr?bner and Sagbi degenerations in the transfer of homological and enumerative information from Stanley-Reisner and/or toric rings to those objects that degenerate to them.作者: capsaicin 時間: 2025-3-23 20:57 作者: 吃掉 時間: 2025-3-24 00:35
,Determinantal Ideals and?the?Straightening Law,In this chapter gives a short introduction to standard bitableaux and the straightening law. This powerful technique is the key to structural properties of determinantal rings. But it is also of central importance for the computation of Gr?bner and Sagbi bases on the one hand and for the representation theoretic approach on the other.作者: 遣返回國 時間: 2025-3-24 06:18
,Universal Gr?bner Bases,Chapter 5 covers the existence of universal Gr?bner bases of determinantal ideals as far as they are known, namely maximal minors and 2-minors. The approach to the case of maximal minors is particularly simple.作者: 肉體 時間: 2025-3-24 09:21
Winfried Bruns,Aldo Conca,Matteo VarbaroCombines representation theoretic and geometric methods to study determinantal varieties.Explores the theoretical use of Gr?bner and Sagbi bases.Contains everything you always wanted to know about Cas作者: 熱心 時間: 2025-3-24 13:34 作者: PLIC 時間: 2025-3-24 18:29 作者: 侵略 時間: 2025-3-24 19:42 作者: 歌唱隊 時間: 2025-3-25 00:42 作者: MARS 時間: 2025-3-25 03:52
https://doi.org/10.1007/978-3-319-77568-5short introduction. It exploits the information on the initial ideal for structural results with a homological flavor, as well as in the computation of enumerative data such as multiplicities and Hilbert series. We give also a more recent approach to Gr?bner bases of determinantal ideals via secant 作者: 瑪瑙 時間: 2025-3-25 08:42 作者: 舊石器時代 時間: 2025-3-25 14:44 作者: GET 時間: 2025-3-25 16:12 作者: finite 時間: 2025-3-25 21:50
Ken Huang,Grace Huang,Adam Dawson,Daniel Wuhasis on vanishing statements. We develop the theory in the relative setting, which offers significant flexibility for the inductive arguments that we employ. We also introduce Schur functors and explain their relationship to direct images of line bundles associated to dominant weights. We end with 作者: Nebulizer 時間: 2025-3-26 01:05 作者: xanthelasma 時間: 2025-3-26 05:33 作者: GRIEF 時間: 2025-3-26 11:35
https://doi.org/10.1007/978-3-031-05480-8Determinantal varieties; Determinantal ideals; Determinantal rings; Sagbi bases; initial ideals; initial 作者: Generalize 時間: 2025-3-26 15:54 作者: Derogate 時間: 2025-3-26 17:34 作者: infatuation 時間: 2025-3-26 22:10
Algebras Defined by Minors,rated by minors through their initial algebras. Since the initial algebras are normal monoid domains, toric algebra can be applied to them. Since normal monoid domains are very well understood, we can draw strong consequences for the algebras defined by minors.作者: enflame 時間: 2025-3-27 01:13
Book 2022h tools from combinatorics, algebra, representation theory and geometry..After a concise introduction to Gr?bner and Sagbi bases, determinantal ideals are studied via the standard monomial theory and the straightening law. This opens the door for representation theoretic methods, such as the Robinso作者: 俗艷 時間: 2025-3-27 08:47 作者: 不出名 時間: 2025-3-27 12:01
The Impact on Major Industries, to the rationality of singularities in characteristic 0, so that we can at least briefly discuss this property for determinantal rings. F-rationality is a very handy tool for the exploitation of toric and equivariant deformations.作者: 勉勵 時間: 2025-3-27 13:55 作者: Deceit 時間: 2025-3-27 20:18 作者: phytochemicals 時間: 2025-3-27 23:15
Asymptotic Regularity for Symbolic Powers of Determinantal Ideals, the asymptotic regularity. We end Chapter 10 with a brief survey of several other homological and arithmetic properties of determinantal ideals that can be derived in a compact way via geometric arguments.作者: resuscitation 時間: 2025-3-28 05:06
,Cohomology and Regularity in?Characteristic Zero,ion of the calculation of Ext modules, we explain how to describe the GL-structure for the local cohomology with support in determinantal ideals. Finally, we conclude the book with a quick survey of the important topic of free resolutions of determinantal ideals.作者: integral 時間: 2025-3-28 08:35 作者: 口訣 時間: 2025-3-28 13:09 作者: 輕觸 時間: 2025-3-28 15:07
Ken Huang,John Yeoh,Sean Wright,Henry Wangts of ideals. In the context of determinantal rings we are mainly interested in linear free resolutions of powers of ideals of maximal minors in the non-generic case, exemplified by ideals of rational normal scrolls.作者: 推遲 時間: 2025-3-28 21:15 作者: Morbid 時間: 2025-3-28 22:55
An Overview on Large Language Modelsion of the calculation of Ext modules, we explain how to describe the GL-structure for the local cohomology with support in determinantal ideals. Finally, we conclude the book with a quick survey of the important topic of free resolutions of determinantal ideals.作者: ethereal 時間: 2025-3-29 04:23
1439-7382 se ring and then applied to powers and products of ideals. The remainder of the book focuses on algebraic geometry, where general vanishing results for the cohomology of line bundles on flag varieties are prese978-3-031-05482-2978-3-031-05480-8Series ISSN 1439-7382 Series E-ISSN 2196-9922 作者: 吵鬧 時間: 2025-3-29 08:42 作者: 元音 時間: 2025-3-29 15:05 作者: interlude 時間: 2025-3-29 19:14
