What does this research mean for the field?

A one-parameter cohomological deformation using Segre-Schwartz-MacPherson (SSM) classes generalizes classical double point formulas, and a newly introduced 'slant sum' operation for quiver gauge theories yields a branching rule for quasimap vertex functions. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

The primary aim is to connect representation theory with enumerative algebraic geometry through the study of SSM classes and their applications.

May 31, 2026Open Access

Enumerative Geometry: SSM Classes of Multisingularities and Curve Counting

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Authors

RLReese LanceUniversity of North Carolina at Chapel Hill

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Implication

This thesis explores SSM classes and their applications in algebraic geometry and gauge theories, revealing new relationships.

Key Points

The primary aim is to connect representation theory with enumerative algebraic geometry through the study of SSM classes and their applications.
Analyzed double point loci of maps between complex manifolds using SSM classes.
Computed SSM-Thom polynomials for singularities and investigated cohomological deformations.
Introduced a slant sum operation between quiver gauge theories and derived a branching rule for vertex functions.
Extended classical double point formulas using SSM classes, improving upon previous results by Fulton and Laksov.
Derived new relationships between vertex functions and quiver varieties through the slant sum operation.
Showed implications of the results on 3d mirror symmetry and factorization corollaries for quiver varieties.

Cite This Study

Reese Lance (2026) studied this question.

synapsesocial.com/papers/6a1bd12d5783ba022b6fcbfe https://doi.org/10.17615/qcnd-br54

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Enumerative Geometry: SSM Classes of Multisingularities and Curve Counting

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Key Points

Cite This Study

Enumerative Geometry: SSM Classes of Multisingularities and Curve Counting

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Member takes

Implication

Key Points

Cite This Study

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