科研之友
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摘要
The classical Severi degree counts the number of algebraic curves of fixed genus and class passing through points in a surface. We express the Severi degrees of P-1 x P-1 as matrix elements of the exponential of a single operator M-S on Fock space. The formalism puts Severi degrees on a similar footing as the more developed study of Hurwitz numbers of coverings of curves. The pure genus 1 invariants of the product E x P-1 (with E an elliptic curve) are solved via an exact formula for the eigenvalues of MS to initial order. The Severi degrees of P-2 are also determined by M-S via the (-1)(d-1)/d(2) disk multiple cover formula for Calabi-Yau threefold geometries.
- 出版日期2017-3
