Skip to content
DraconiticResearch
Search Sources API
203,203 studies31 sourcesUpdated 55 min ago
PreprintarXiv licencearXiv

The Geometric Arveson-Douglas Conjecture through Veronese Embeddings

  • Francesca Arici
  • Yufan Ge
  • Dimitris Michail Gerontogiannis
Open at sourcePDFDOICite

Abstract

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 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.

Related

  1. Commutative Counterexamples to Arveson's Hyperrigidity Conjecture
    Boris Bilich, Marcel Scherer
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  2. On Douglas' conjecture for m-Kronecker quivers
    So Okada
    arXivPreprintarXiv licenceFull textAlgebra & number theoryCombinatorics & discrete mathematicsarXiv
  3. Transfer of similarity to Hilbert space contractions through inner functions: a proof of Douglas's conjecture
    Catalin Badea
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsarXiv
  4. Representation embeddings and the third Brauer--Thrall conjecture
    Haruhisa Enomoto
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  5. The Yau Geometric Conjecture for Isolated Hypersurface Singularities
    Siyuan Fu, Stephen S. -T. Yau, Huaiqing Zuo
    arXivPreprintCC BY-NC-ND 4.0Full textAlgebra & number theoryarXiv

Cite

BibTeXRIS
BibTeX
@misc{arici2026geometric,
  title = {{The Geometric Arveson-Douglas Conjecture through Veronese Embeddings}},
  author = {Francesca Arici and Yufan Ge and Dimitris Michail Gerontogiannis},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.09836},
  eprint = {2610.09836},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.09836},
}
RIS
TY  - UNPB
TI  - The Geometric Arveson-Douglas Conjecture through Veronese Embeddings
AU  - Francesca Arici
AU  - Yufan Ge
AU  - Dimitris Michail Gerontogiannis
PY  - 2026
DA  - 2026/10/07
PB  - arXiv
DO  - 10.48550/arxiv.2610.09836
UR  - https://arxiv.org/abs/2610.09836
AB  - 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 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.
ER  -