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Creators/Authors contains: "Chen, Qile"

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  1. ; ; ; (, EMS press)
    We introduce a variant of stable logarithmic maps, which we call punctured logarith- mic maps. They allow an extension of logarithmic Gromov–Witten theory in which marked points have a negative order of tangency with boundary divisors. As a main application we develop a gluing formalism which reconstructs stable logarithmic maps and their virtual cycles without expansions of the target, with trop- ical geometry providing the underlying combinatorics. Punctured Gromov–Witten invariants also play a pivotal role in the intrinsic con- struction of mirror partners by the last two authors, conjecturally relating to symplec- tic cohomology, and in the logarithmic gauged linear sigma model in work of Qile Chen, Felix Janda and Yongbin Ruan. 
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    Free, publicly-accessible full text available February 5, 2026
  2. ; ; ; (, Geometry & Topology)
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  3. ; ; (, Advances in Mathematics)
    null (Ed.)
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  4. ; ; (, Inventiones mathematicae)
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  5. ; ; ; (, Compositio Mathematica)
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    We prove a decomposition formula of logarithmic Gromov–Witten invariants in a degeneration setting. A one-parameter log smooth family $$X \longrightarrow B$$ with singular fibre over $$b_0\in B$$ yields a family $$\mathscr {M}(X/B,\beta ) \longrightarrow B$$ of moduli stacks of stable logarithmic maps. We give a virtual decomposition of the fibre of this family over $$b_0$$ in terms of rigid tropical maps to the tropicalization of $X/B$ . This generalizes one aspect of known results in the case that the fibre $$X_{b_0}$$ is a normal crossings union of two divisors. We exhibit our formulas in explicit examples. 
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  6. ; ; ; ; (, Macromolecules)
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  7. ; (, Journal für die reine und angewandte Mathematik (Crelles Journal))
    Abstract In this paper, we study {\mathbb{A}^{1}} -connected varieties from log geometry point of view, and prove a criterion for {\mathbb{A}^{1}} -connectedness. As applications, we provide many interesting examples of {\mathbb{A}^{1}} -connected varieties in the case of complements of ample divisors, and the case of homogeneous spaces. We also obtain a logarithmic version of Hartshorne conjecture characterizing projective spaces and affine spaces. 
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  8. ; (, Selecta Mathematica)
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  9. ; (, Annales de l'Institut Fourier)
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  10. ; (, Journal of Algebraic Geometry)
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