Local BPS Invariants: Enumerative Aspects and Wall-Crossing

Jinwon Choi; Michel van Garrel; Sheldon Katz; Nobuyoshi Takahashi

doi:10.1093/imrn/rny171

Local BPS Invariants: Enumerative Aspects and Wall-Crossing

Jinwon Choi, Michel van Garrel, Sheldon Katz, Nobuyoshi Takahashi

Research output: Contribution to journal › Article › peer-review

Abstract

We study the BPS invariants for local del Pezzo surfaces, which can be obtained as the signed Euler characteristic of the moduli spaces of stable one-dimensional sheaves on the surface S⁠. We calculate the Poincaré polynomials of the moduli spaces for the curve classes β having arithmetic genus at most 2. We formulate a conjecture that these Poincaré polynomials are divisible by the Poincaré polynomials of ((−KS).β−1)-dimensional projective space. This conjecture motivates the upcoming work on log BPS numbers [8].

Original language	English (US)
Pages (from-to)	5450-5475
Number of pages	26
Journal	International Mathematics Research Notices
Volume	2020
Issue number	17
DOIs	https://doi.org/10.1093/imrn/rny171
State	Published - Sep 2020

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Mathematics(all)

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abstract = "We study the BPS invariants for local del Pezzo surfaces, which can be obtained as the signed Euler characteristic of the moduli spaces of stable one-dimensional sheaves on the surface S⁠. We calculate the Poincar{\'e} polynomials of the moduli spaces for the curve classes β having arithmetic genus at most 2. We formulate a conjecture that these Poincar{\'e} polynomials are divisible by the Poincar{\'e} polynomials of ((−KS).β−1)-dimensional projective space. This conjecture motivates the upcoming work on log BPS numbers [8].",

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AB - We study the BPS invariants for local del Pezzo surfaces, which can be obtained as the signed Euler characteristic of the moduli spaces of stable one-dimensional sheaves on the surface S⁠. We calculate the Poincaré polynomials of the moduli spaces for the curve classes β having arithmetic genus at most 2. We formulate a conjecture that these Poincaré polynomials are divisible by the Poincaré polynomials of ((−KS).β−1)-dimensional projective space. This conjecture motivates the upcoming work on log BPS numbers [8].

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Local BPS Invariants: Enumerative Aspects and Wall-Crossing

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