6 papers · 1 filter
Refined curve counting with descendants and quantum mirrors
Patrick Kennedy-Hunt, Qaasim Shafi, Ajith Urundolil Kumaran
Given a log Calabi--Yau surface , Bousseau has constructed a quantization of the mirror algebra of this pair. We give a formula for structure constants of this quantization…
Coherent sheaves in logarithmic geometry
Hannah Dell, Xianyu Hu, Patrick Kennedy-Hunt +2
This paper introduces an abelian category of logarithmic coherent sheaves that arranges coherent sheaves across all expansions and root stacks of a simple normal crossing degenerat…
The Logarithmic Quot space: foundations and tropicalisation
Patrick Kennedy-Hunt
We construct a logarithmic version of the Hilbert scheme, and more generally the Quot scheme, of a simple normal crossings pair. The logarithmic Quot space admits a natural tropica…
Logarithmic Quot spaces, boundedness, and K-tropicalizations
Patrick Kennedy-Hunt, Dhruv Ranganathan
Logarithmic Hilbert and Quot spaces are generalizations of their traditional versions adapted to study pairs and degenerations. The logarithmic Quot spaces of parameterize…
Tropical refined curve counting with descendants
Patrick Kennedy-Hunt, Qaasim Shafi, Ajith Urundolil Kumaran
We prove a -refined tropical correspondence theorem for higher genus descendant logarithmic Gromov--Witten invariants with a class in toric surfaces. Specifically, a gene…
Divisors and curves on logarithmic mapping spaces
Patrick Kennedy-Hunt, Navid Nabijou, Qaasim Shafi +1
We determine the rational class and Picard groups of the moduli space of stable logarithmic maps in genus zero, with target projective space relative a hyperplane. For the class gr…