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Author Givental, Alexander
Source CiteSeerX
Content type Text
File Format PDF
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Recent Result ♦ Gromov-witten Invariant ♦ Torus-equivariant Gromov Witten Invariant ♦ Compact Ka Hler Manifold ♦ Complex Oscillating Integral ♦ Non-linear Serre Duality Theorem ♦ Toric Manifold ♦ Extensive Footnote ♦ New Proof ♦ Elliptic Gromov Witten Invariant ♦ Concave Bundle Space ♦ Quintic 3-folds ♦ Generalized Mirror Conjecture ♦ Several Result ♦ Isolated Fixed Point ♦ Semi-simple Frobenius Structure ♦ Mirror-theoretic Term ♦ Gromov Witten Theory Include ♦ Mirror Conjecture ♦ Mirror Theorem
Description A conjecture expressing genus 1 Gromov-Witten invariants in mirror-theoretic terms of semi-simple Frobenius structures and complex oscillating integrals is formulated. The proof of the conjecture is given for torus-equivariant Gromov- Witten invariants of compact Kähler manifolds with isolated fixed points and for concave bundle spaces over such manifolds. Several results on genus 0 Gromov- Witten theory include: a non-linear Serre duality theorem, its application to the genus 0 mirror conjecture, a mirror theorem for concave bundle spaces over toric manifolds generalizing a recent result of B. Lian, K. Liu and S.-T. Yau. We also establish a correspondence (see the extensive footnote in section 4) between their new proof of the genus 0 mirror conjecture for quintic 3-folds and our proof of the same conjecture given two years ago.
Educational Role Student ♦ Teacher
Age Range above 22 year
Educational Use Research
Education Level UG and PG ♦ Career/Technical Study
Learning Resource Type Article
Publisher Date 1998-01-01
Publisher Institution In: Integrable Systems and Algebraic Geometry. World Sci. Publ., River Edge, NJ