Certified Severi dimensions for hyperelliptic and supersymmetric cusps
Ethan Cotterill, Vin\'icius Lima, Renato Vidal Martins, and Alexandre, Reis

TL;DR
This paper proves a conjecture about the dimensions of certain moduli spaces of holomorphic maps with specific cusp singularities, focusing on hyperelliptic and supersymmetric cases.
Contribution
It establishes that an adjusted form of a conjecture on Severi variety dimensions holds for generic profiles related to two classes of semigroups.
Findings
Confirmed the conjecture for generic profiles in hyperelliptic cases.
Extended the conjecture to supersymmetric cusp cases.
Provided explicit dimension formulas for these classes.
Abstract
In a previous paper, the first three authors formulated a precise conjecture about the dimension of the {\it generalized Severi variety} of degree- holomorphic maps whose images' singularities are singleton cusps with value semigroups and ramification profiles . In this paper, we prove that an adjusted form of the conjecture holds for generic profiles associated with two distinguished (infinite) classes of semigroups .
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Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic Geometry and Number Theory · Geometry and complex manifolds
