Quantum Spectral Curve for the Gromov-witten Theory of the Complex Projective Line
نویسنده
چکیده
We construct the quantum curve for the Gromov-Witten theory of the complex projective line.
منابع مشابه
Convergence of Quantum Cohomology by Quantum Lefschetz
Quantum Lefschetz theorem by Coates and Givental [4] gives a relationship between the genus 0 Gromov-Witten theory of X and the twisted theory by a line bundle L on X. We prove the convergence of the twisted theory under the assumption that the genus 0 theory for original X converges. As a byproduct, we prove the semisimplicity and the Virasoro conjecture for the Gromov-Witten theories of (not ...
متن کاملQuantum Kirwan Morphism and Gromov-witten Invariants of Quotients Ii
This is the second in a sequence of papers in which we construct a quantum version of the Kirwan map from the equivariant quantum cohomology QHG(X) of a smooth polarized complex projective variety X with the action of a connected complex reductive group G to the orbifold quantum cohomology QH(X//G) of its geometric invariant theory quotient X//G, and prove that it intertwines the genus zero gau...
متن کاملQuantum Kirwan Morphism and Gromov-witten Invariants of Quotients I
This is the first in a sequence of papers in which we construct a quantum version of the Kirwan map from the equivariant quantum cohomology QHG(X) of a smooth polarized complex projective variety X with the action of a connected complex reductive group G to the orbifold quantum cohomology QH(X//G) of its geometric invariant theory quotient X//G, and prove that it intertwines the genus zero gaug...
متن کاملJ ul 2 00 9 AREA DEPENDENCE IN GAUGED GROMOV - WITTEN THEORY
We prove a wall-crossing formula for the variation of gauged GromovWitten invariants of a smooth projective G-variety (with fixed domain curve) with respect to the natural stability condition defined by the area of the curve. As an application, we prove a gauged version of the abelianization (or quantum Martin) conjecture of Bertram, Ciocan-Fontanine, and Kim [8], which relates GromovWitten inv...
متن کاملK-theoretic J-functions of Type a Flag Varieties
The J-function in Gromov-Witten theory is a generating function for one-point genus zero Gromov-Witten invariants with descendants. Here we give formulas for the quantum K-theoretic J-functions of type A flag manifolds. As an application, we prove the quantum K-theoretic J-function version of the abelian-nonabelian correspondence for Grassmannians and products of projective space.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2013