Enumerating log rational curves on some toric varieties

Carl Lian; Naufil Sakran

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arXiv · 2506.13975

Enumerating log rational curves on some toric varieties

Carl Lian·Naufil Sakran

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Abstract

The genus 0, fixed-domain log Gromov-Witten invariants of a smooth, projective toric variety X enumerate maps from a general pointed rational curve to a smooth, projective toric variety passing through the maximal number of general points and with prescribed multiplicities along the toric boundary. We determine these invariants completely for the projective bundle X=P_{P^r}(O^s+O(-a)), proving a conjecture of Cela--Iribar L\'opez. A different conjecture when X is the blow-up of P^r at r points is disproven. Whereas the conjectures were predicted using tropical methods, we give direct intersection-theoretic calculations on moduli spaces of "naive log quasimaps."

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BibTeX RIS

Carl Lian, Naufil Sakran. 2025-06-16. Enumerating log rational curves on some toric varieties. https://arxiv.org/abs/2506.13975

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