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math.AG2026
Nonlinear neighborhoods of smooth curves and arbitrarily negative Wahl defects
Heesang Park, Dongsoo Shin
We develop a theory of nonlinear neighborhoods of smooth projective curves of genus at least two, constructed by gluing products of open subsets of a curve with a disc using nonlin…
math.AG2026
Positivity of Wahl defects and specialization of reflexive powers of the canonical sheaf
Heesang Park, Dongsoo Shin
Let be the minimal good resolution of a normal complex surface singularity, with reduced. The Wahl defect is $Δ(V,0) :=h^1(\mathcal{O}_X)-h^1(S_X)+h^1(\bigwed…
math.AG2026
Normal complex surface singularities with rational homology disk smoothings
Márton Beke, Heesang Park, Dongsoo Shin +1
We prove that a normal surface singularity whose minimal good resolution graph has at least two nodes does not admit a rational homology disk smoothing. Together with the earlier g…