发表机构
Leiden University（莱顿大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明几何Arveson-Douglas猜想在Veronese嵌入下不变，提供奇异簇新例，并归结到二次Gröbner基情形，同时证明基本类猜想不变性并给出无穷反例。
AI 中文摘要
我们证明了射影簇的Veronese嵌入下几何Arveson-Douglas猜想的不变性。这提供了满足该猜想的奇异簇的新例子。此外，通过保持相同的Schatten正则性阈值，它将猜想归结为定义理想具有二次Gröbner基的射影簇。我们的结果导致了子积系统的典范例子，其Toeplitz代数与复数不$KK$-等价。最后，我们证明了Douglas基本类猜想（断言相关的Toeplitz扩张在$KK$-理论中实现$\mathbb{T}$-等变对偶）在Veronese嵌入下也是不变的。虽然后一结果自举了基本类猜想，但它也导致了无穷多个反例。
英文摘要
We prove invariance of the geometric Arveson-Douglas conjecture under Veronese embeddings of projective varieties. This provides new examples of singular varieties satisfying the conjecture. Furthermore, it reduces the conjecture to projective varieties whose defining ideals admit quadratic Gr{ö}bner bases, by keeping the same Schatten regularity thresholds. Our results lead to canonical examples of subproduct-systems whose Toeplitz algebras are not $KK$-equivalent to the complex numbers. Finally, we show that Douglas' fundamental class conjecture, asserting that the associated Toeplitz extension implements $\mathbb{T}$-equivariant duality in $KK$-theory, is invariant under Veronese embeddings as well. While the latter result bootstraps the fundamental class conjecture, it also leads to infinitely many counterexamples.
Comments18 pages
