Rational Curves on the Space of Determinantal Nets of Conics

Details Rational Curves on the Space of Determinantal Nets of Conics Rational Curves on the Space of Determinantal Nets of Conics

1998-02-06

arxiv.org/abs/math/9802037v1

Mathematics

Algebraic Geometry

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

Scientific paper

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.

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