A closed Euler product formula for the genus set cardinality of Gorenstein cubic orders is derived via explicit local overorder classification.
Altman and Steven L
4 Pith papers cite this work, alongside 362 external citations. Polarity classification is still indexing.
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The algebraic stratification of Hitchin fibers via local smoothening types is proven equivalent to the geometric stratification by partial normalizations for GL_n in the Bass case, yielding an explicit cohomology formula for compactified Jacobians of spectral curves with double singularities.
For the standard representation of Sp_{2n}(C), the Gaiotto locus is the Bialynicki-Birula closure associated to U(Sp_{2n-2}(C)) inside the nilpotent cone, and its intersection with the stable cotangent chart is the closure of the conormal bundle to the one-spinor stratum of the generalized theta-div
Stable pairs yield small Q-factorial modifications of Quot schemes on curves, making their large-degree fibers Mori dream spaces and the determinant morphism a Mori dream morphism.
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Ideal class monoids of cubic orders
A closed Euler product formula for the genus set cardinality of Gorenstein cubic orders is derived via explicit local overorder classification.
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Global geometrization of local smooth integral models in the Hitchin fibration for $\mathrm{GL}_n$: The Bass case
The algebraic stratification of Hitchin fibers via local smoothening types is proven equivalent to the geometric stratification by partial normalizations for GL_n in the Bass case, yielding an explicit cohomology formula for compactified Jacobians of spectral curves with double singularities.
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Gaiotto Loci and the Nilpotent Cone for $\mathrm{Sp}_{2n}(\mathbb C)$
For the standard representation of Sp_{2n}(C), the Gaiotto locus is the Bialynicki-Birula closure associated to U(Sp_{2n-2}(C)) inside the nilpotent cone, and its intersection with the stable cotangent chart is the closure of the conormal bundle to the one-spinor stratum of the generalized theta-div
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Birational Geometry of Quot Schemes on smooth projective curves via Stable Pairs
Stable pairs yield small Q-factorial modifications of Quot schemes on curves, making their large-degree fibers Mori dream spaces and the determinant morphism a Mori dream morphism.