2022/02/01 by Sybille Rosset, Rosset, Sybille · 2 citations
Mathematics · #Advanced Combinatorial Mathematics #Algebra over a field #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Combinatorics #Commutative Algebra and Its Applications #Degree (music) #Equivariant map #Euler characteristic #FOS: Mathematics #Fibration #Flag (linear algebra) #Hyperplane #Linear subspace #Mathematical analysis #Mathematics #Physics #Pure mathematics #Quantum #Quantum mechanics #Ring (chemistry) #Subspace topology #Variety (cybernetics) #math.AG
paper · pdf · doi:10.48550/arxiv.2202.00773
published in arXiv (Cornell University) (Cornell University) · PhD thesis
arxiv created 2022/02/01 · openalex publication_date 2022/02/01 · arxiv updated 2022/02/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/08
Forgetting a subspace from a partial flag yields another partial flag composed of fewer subspaces. This induces a forgetful map π: X → X' between the corresponding flag varieties. We prove here that, for a degree large enough, the variety associated with degree d stable maps sending their marked points within Schubert varieties Xi of X is a rationally connected fibration over its image, which parametrizes degree π_* d stable maps sending their marked points within the Schubert varieties π(Xi) of X'. The Euler characteristic of these varieties are quantum K-invariants. Our result implies equalities between quantum K correlators. We extend these equalities to the equivariant setting. Finally, we study the small quantum K-ring of the universal hyperplane Fl1,n-1. We prove a Chevalley formula in QKs(Fl1,n-1) via geometrical analysis of the space of stale maps to Fl1,n-1 and of its image via evaluation maps.