Smoothness of Severi Varieties

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.