The Hermitian Distance degree of an Algebraic Variety

Mathematics > Algebraic Geometry [Submitted on 22 Oct 2025 (v1), last revised 18 Jun 2026 (this version, v2)] Title:The Hermitian Distance degree of an Algebraic Variety View PDF HTML (experimental)Abstract:In this paper we develop an algebraic theory to study the problem of finding the minimum distance point from an algebraic variety with respect to the Hermitian distance function. The theory generalizes the Euclidean Distance degree introduced in arXiv:1309.0049, replacing a positive symmetric bilinear form by a Hermitian form. Various examples are presented to show the robustness of the machinery. Submission history From: Davide Furchì [view email][v1] Wed, 22 Oct 2025 10:49:11 UTC (118 KB) [v2] Thu, 18 Jun 2026 11:35:03 UTC (146 KB) References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer (What is the Explorer?) Connected Papers (What is Connected Papers?) Litmaps (What is Litmaps?) scite Smart Citations (What are Smart Citations?) Code, Data and Media Associated with this Article alphaXiv (What is alphaXiv?) CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub (What is DagsHub?) Gotit.pub (What is GotitPub?) Hugging Face (What is Huggingface?) ScienceCast (What is ScienceCast?) Demos Recommenders and Search Tools Influence Flower (What are Influence Flowers?) CORE Recommender (What is CORE?) arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.