Local BPS invariants: enumerative aspects and wall-crossing
J Choi, M van Garrel, S Katz… - International …, 2020 - academic.oup.com
J Choi, M van Garrel, S Katz, N Takahashi
International Mathematics Research Notices, 2020•academic.oup.comWe 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. We calculate the Poincaré polynomials of the moduli spaces for the curve classes
having arithmetic genus at most 2. We formulate a conjecture that these Poincaré
polynomials are divisible by the Poincaré polynomials of-dimensional projective space. This
conjecture motivates the upcoming work on log BPS numbers.
signed Euler characteristic of the moduli spaces of stable one-dimensional sheaves on the
surface. We calculate the Poincaré polynomials of the moduli spaces for the curve classes
having arithmetic genus at most 2. We formulate a conjecture that these Poincaré
polynomials are divisible by the Poincaré polynomials of-dimensional projective space. This
conjecture motivates the upcoming work on log BPS numbers.
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 . We calculate the Poincaré polynomials of the moduli spaces for the curve classes having arithmetic genus at most 2. We formulate a conjecture that these Poincaré polynomials are divisible by the Poincaré polynomials of -dimensional projective space. This conjecture motivates the upcoming work on log BPS numbers .
Oxford University Press