A refinement of the stable pair invariants of Pandharipande and Thomas for non-compact
Calabi–Yau spaces is introduced based on a virtual Bialynicki-Birula decomposition with …

Refined curve counting with tropical geometry Page 1 Refined curve counting with tropical
geometry Florian Block and Lothar Göttsche Compositio Math. 152 (2016), 115–151. doi:10.1112/S0010437X1500754X …

Block and Göttsche have defined aq-number refinement of counts of tropical curves in R^ 2
R 2. Under the change of variables q= e^ iu q= e iu, we show that the result is a generating …

We prove aq-refined tropical correspondence theorem for higher genus descendant
logarithmic Gromov–Witten invariants with a λ g class in toric surfaces. Specifically, a …

The Quot scheme of points $\mathrm {Quot} _ {d, n}(X) $ on a variety $ X $ over a field $ k $
parametrizes quotient sheaves of $\mathcal {O} _X^{\oplus d} $ of zero-dimensional support …

We consider two motivic generating functions defined on a variety, and reveal their tight
connection. They essentially count torsion-free bundles and zero-dimensional sheaves. On …

On Block–Gottsche Multiplicities for Planar Tropical Curves Page 1 I. Itenberg and G.
Mikhalkin (2013) “On Block–G öttsche Multiplicities for Planar Tropical Curves,” …

Quot schemes of quotients of a trivial bundle of arbitrary rank on a nonsingular projective
surface X carry perfect obstruction theories and virtual fundamental classes whenever the …

Abstract In the Gross–Siebert mirror symmetry program, certain enumerations of tropical
disks are encoded in combinatorial objects called scattering diagrams and broken lines …

We associate a half-integer number, called the quantum index, to algebraic curves in the
real plane satisfying to certain conditions. The area encompassed by the logarithmic image …