For any smooth projective toric variety, a contraction morphism from stable maps to quasimaps is constructed on a closed substack, and is proven surjective when the target is Fano.
Derived moduli of sections and push-forwards
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abstract
We introduce a derived enhancement of the moduli space of sections defined by Chang-Li, and we compute its tangent complex. Special cases of this moduli space include stable maps and stable quasi-maps. As an application, we prove that G-theoretic stable map and quasi-map invariants of projective spaces are equal.
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The contraction morphism between maps and quasimaps to toric varieties
For any smooth projective toric variety, a contraction morphism from stable maps to quasimaps is constructed on a closed substack, and is proven surjective when the target is Fano.