发表机构
Morningside Center of Mathematics, Chinese Academy of Sciences; Department of Mathematics, The University of Hong Kong（中国科学院数学与系统科学研究院; 香港大学数学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究在任意域上构造了拉斯科、正格罗滕迪克等多项式的可实现体积模型，证明了多个相关支集与牛顿多面体猜想，还得到全局生成丛最高次全陈多项式的可实现性结论。
AI 中文摘要
我们在任意域上为阶乘归一化的齐次拉斯科（Lascoux）多项式、拉斯科原子（Lascoux-atom）多项式以及正格罗滕迪克（positive Grothendieck）多项式组构造了可实现体积模型。它们的体积子式包含归一化关键多项式、德马祖尔原子（Demazure atoms）多项式、舒伯特（Schubert）多项式以及所有符号校正的齐次格罗滕迪克分量。在复数域（$\boldsymbol{\text{C}}$）上，这些多项式是洛伦兹型的。作为推论，普通格罗滕迪克多项式、拉斯科多项式与拉斯科原子多项式的支集是$M^{\natural}$-凸的，且恰好是其积分广义拟阵牛顿多面体的格点。这以更强的可实现体积形式证明了Huh–Matherne–Mészáros–St.~Dizier提出的对应猜想，以及Monical–Tokcan–Yong、Mészáros–St.~Dizier、Mészáros–Setiabrata–St.~Dizier提出的相关饱和牛顿多面体与格罗滕迪克支集猜想。最大次数的格罗滕迪克分量作为特例给出了卡斯泰尔诺沃–穆姆福德（Castelnuovo–Mumford）支集猜想。我们的方法还产生了有限对偶为可实现体积多项式的更多多项式组。更一般地，在任意域上，全局生成丛的阶乘归一化最高次全陈（total-Chern）多项式是可实现体积多项式，且我们的齐次实现的支集是代数拟阵的基。
英文摘要
We construct realizable-volume models over every field for the factorial normalizations of homogeneous Lascoux, Lascoux-atom, and positive Grothendieck packets, including their minimal homogenizations and layers. In particular, the construction realizes the factorial normalizations of all Schubert and key polynomials and of the minimal sign-corrected homogeneous Grothendieck polynomials. The normalized polynomials are Lorentzian, and the ordinary supports are the lattice points of integral generalized polymatroids. On a Bott--Samelson tower, row and co-row filtrations assemble the local factors into globally generated bundles; a creation-state graph absorbs the remaining kernel factors by Chern flow. We also construct intrinsic algebras of joint Chern moments. Positive inverse-Chern presentations give these algebras Hard Lefschetz and Hodge--Riemann relations, and supply source-level Hodge completions of the packets. For globally generated tropical toric bundles in the sense of Kaveh--Manon, finite generating witnesses and matroid duality provide the presentations required by Larson--Partida's theorem, without representability. These constructions yield joint Chern-number inequalities, nonvanishing polymatroids, and equality criteria.
Comments74 pages. Comments are welcome
