
TL;DR
This paper provides a rigorous proof of the smoothness and dimension properties of Severi varieties, addressing gaps in existing literature using a combination of algebraic and analytic techniques.
Contribution
It offers a new, rigorous proof of Severi varieties' smoothness and dimension, filling gaps in standard proofs with a novel algebraic-analytic approach.
Findings
Confirmed smoothness of Severi varieties under certain conditions
Established the expected dimension of Severi varieties
Bridged gaps in previous proofs with a rigorous method
Abstract
We aim at giving a rigorous proof of the state-ments on the smoothness and the dimension of Severi varieties wherethere are gaps in the proofs in some standard literature. The method isa mixture of algebraic and analytic methods.
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Taxonomy
TopicsPolynomial and algebraic computation · Advanced Numerical Analysis Techniques · Algebraic Geometry and Number Theory
