6 citations · 11 across the 4 of their papers we have counts for
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Counting Plane Rational Curves: Old and New Approaches
Aleksey Zinger
These notes are intended as an easy-to-read supplement to part of the background material presented in my talks on enumerative geometry. In particular, the numbers and …
On the Genus-One Gromov-Witten Invariants of Complete Intersections
Jun Li, Aleksey Zinger
As shown in a previous paper, certain naturally arising cones of holomorphic vector bundle sections over the main component $\ov\M_{1,k}^0(¶,d)$ of the moduli space of stable genus…
On the Genus-One Gromov-Witten Invariants of a Quintic Threefold
Jun Li, Aleksey Zinger
We rederive a relation between the genus-one GW-invariants of a quintic threefold in $\Pf$ and the genus-zero and genus-one GW-invariants of $\Pf$. In contrast to the more general…
Enumeration of One-Nodal Rational Curves in Projective Spaces
A. Zinger
We give a formula computing the number of one-nodal rational curves that pass through an appropriate collection of constraints in a complex projective space. We combine the methods…
Completion of Katz-Qin-Ruan's Enumeration of Genus-Two Plane Curves
A. Zinger
We give a formula for the number of genus-two fixed-complex-structure degree-d plane curves passing through 3d-2 points in general position. This is achieved by completing Katz-Qin…