2015/09/30 by Richard Lärkäng, Jean Ruppenthal
Mathematics · #Affine transformation #Algebra over a field #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #Compact space #Gravitational singularity #Homotopy #Mathematical analysis #Mathematics #Operator (biology) #Projective test #Pure mathematics #math.CV #msc:32A26 #msc:32A27 #msc:32B15 #msc:32C30 #msc:32W05
paper · pdf · doi:10.1512/iumj.2018.67.6309
published as Indiana Univ. Math. J., 67 (2018), No. 2, 753-780 · 22 pages. v2: corrections from the review process. arXiv admin note: text overlap with arXiv:1407.5703
openalex created_date 2016/06/24 · openalex publication_date 2018/01/01 · arxiv created 2018/04/20 · arxiv updated 2018/04/30 · openalex updated_date 2026/08/05
In the present paper, we study regularity of the Andersson-Samuelsson Koppelman integral operator on affine cones over smooth projective complete intersections. Particularly, we prove L-p- and C-alpha-estimates, and compactness of the operator, when the degree is sufficiently small. As applications, we obtain homotopy formulas for different partial derivative-operators acting on L-p-spaces of forms, including the case p = 2 if the varieties have canonical singularities. We also prove that the A-forms introduced by Andersson-Samuelsson are C-alpha for alpha < 1.