arXiv subjects

Nawaz Sultani

Publications and source records attributed to Nawaz Sultani.

3 recordsLinked to original sources

arXiv2024

Gromov--Witten Invariants of Non-Convex Complete Intersections in Weighted Projective Stacks

In this paper we compute genus 0 orbifold Gromov--Witten invariants of Calabi--Yau threefold complete intersections in weighted projective stacks, regardless of convexity conditions. The traditional quantumn Lefschetz principle may fail even for invariants with ambient insertions. Using quasimap wall-crossing, we are able to compute invariants with insertions from a specific subring of the Chen--Ruan cohomology, which contains all the ambient cohomology classes. Quasimap wall-crossing gives a mirror theorem expressing the I-function in terms of the J-function via a mirror map. The key of this paper is to find a suitable GIT presentation of the target space, so that the mirror map is invertible. An explicit formula for the I-function is given for all those target spaces and many examples with explicit computations of invariants are provided.

math.AG↗

arXiv2023

Some Applications of Abelianization in Gromov-Witten Theory

Let $G$ be a complex reductive group and let $X$ and $E$ be two linear representations of $G$. Let $Y$ be a complete intersection in $X$ equal to the zero locus of a $G$-equivariant section of the trivial bundle $E \times X \to X$. We explain some general techniques for using quasimap formulas to compute useful $I$-functions of $Y\mathord{/\mkern-6mu/} G$. We work several explicit examples, including a rigorous derivation of a quantum period computed conjecturally by Oneto-Petracci.

math.AG↗

arXiv2022

Subtleties of Quantum Lefshetz without Convexity

Let $Y\mathord{/\mkern-6mu/}_θG$ be a complete intersection in a GIT quotient $X\mathord{/\mkern-6mu/}_θG$ cut out by a $G$-representation $E$. We show that the $E$-twisted quasimap $I$-function recovers invariants of $(Y, G, θ)$ if its nonequivariant limit exists before restriction to $Y\mathord{/\mkern-6mu/}_θG$. This corrects a conjecture credited to Coates-Corti-Iritani-Tseng. We explain how to correct computations in the literature based on the faulty conjecture.

math.AG↗