Local and relative BPS state counts for del Pezzo surfaces
Michel van Garrel
TL;DR
This paper explores the relationship between local and relative BPS state counts for del Pezzo surfaces, revealing a linear connection mediated by generalized Donaldson-Thomas invariants of loop quivers, advancing understanding in enumerative geometry.
Contribution
It establishes a linear relation between relative and local BPS counts for del Pezzo surfaces using generalized Donaldson-Thomas invariants, providing new insights into their enumerative geometry.
Findings
Relative BPS counts are linearly related to local BPS counts for del Pezzo surfaces.
Generalized Donaldson-Thomas invariants of loop quivers mediate this relationship.
The results deepen understanding of BPS state counts in log Calabi-Yau surface pairs.
Abstract
Relative BPS state counts for log Calabi-Yau surface pairs were introduced by Gross-Pandharipande-Siebert. We describe how in the case of del Pezzo surfaces they are linearly related to local BPS state counts by means of generalized Donaldson-Thomas invariants of loop quivers.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Algebraic Geometry and Number Theory · Advanced Combinatorial Mathematics