Rational Curves on the Space of Determinantal Nets of Conics

1998/02/06 by Erik N. Tjøtta, Erik N. Tjotta, Tjotta, Erik N. · 3 citations
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Mathematical Dynamics and Fractals #Polynomial and algebraic computation #math.AG #msc:14D20 #msc:14F32 #msc:14M12

paper · pdf · doi:10.48550/arxiv.math/9802037

LaTex. 58 pages. Doctoral dissertation, defended Oktober 1997 at The University of Bergen, Norway

arxiv created 1998/02/06 · arxiv updated 2009/11/30

Abstract

We describe the Hilbert scheme components parametrizing lines and conics on the space of determinantal nets of conics, N. As an application, we use the quantum Lefschetz hyperplane principle to compute the instanton numbers of rational curves on a complete intersection Calabi-Yau threefold in N. We also compute the number of lines and conics on some Calabi-Yau sections of non-decomposable vector bundles on N. The paper contains a brief summary of the A-model theory leading up to Givental-Kim's quantum Lefschetz hyperplane principle.

Cited by

• Quantum Hyperplane Section Theorem For Homogeneous Spaces
• Monodromy of Picard-Fuchs differential equations for Calabi-Yau threefolds
• Quantum cohomology of a Pfaffian Calabi-Yau variety: verifying mirror symmetry predictions
• Monodromy calculatons of fourth order equations of Calabi-Yau type

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