Relative Gromov–Witten and maximal contact conics
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DOI: 10.1007/s00013-025-02169-z
Abstract: We discuss some properties of the relative Gromov–Witten invariants counting rational curves with maximal contact order at one point. We compute the number of Cayley’s sextactic conics to any smooth plane curve. In particular, we… read more here.
Keywords: relative gromov; witten maximal; gromov witten; maximal contact ... See more keywords
Weighted-blowup correspondence of orbifold Gromov–Witten invariants and applications
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DOI: 10.1007/s00208-019-01850-3
Abstract: Let $$\mathsf {X}$$X be a compact symplectic orbifold groupoid with $$\mathsf {S}$$S being a compact symplectic sub-orbifold groupoid, and $${\underline{\mathsf {X}}_{\mathfrak {a}}}$$X̲a be the weight-$${\mathfrak {a}}$$a blowup of $$\mathsf {X}$$X along $$\mathsf {S}$$S with $$\mathsf… read more here.
Keywords: weighted blowup; blowup correspondence; gromov witten; mathsf ... See more keywords
Gromov–Witten theory and Noether–Lefschetz theory for holomorphic-symplectic varieties
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DOI: 10.1017/fms.2022.10
Abstract: Abstract We use Noether–Lefschetz theory to study the reduced Gromov–Witten invariants of a holomorphic-symplectic variety of $K3^{[n]}$ -type. This yields strong evidence for a new conjectural formula that expresses Gromov–Witten invariants of this geometry for… read more here.
Keywords: theory; noether lefschetz; gromov witten; witten theory ... See more keywords
Descendant log Gromov-Witten invariants for toric varieties and tropical curves
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DOI: 10.1090/tran/7936
Abstract: Using degeneration techniques, we prove the correspondence of tropical curve counts and log Gromov-Witten invariants with general incidence and psi-class conditions in toric varieties for genus zero curves. For higher-genus situations, we prove the correspondence… read more here.
Keywords: toric varieties; witten invariants; descendant log; invariants toric ... See more keywords
Relative Gromov–Witten invariants and the enumerative meaning of mirror maps for toric Calabi–Yau orbifolds
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DOI: 10.1090/tran/8196
Abstract: We provide an enumerative meaning of the mirror maps for toric Calabi–Yau orbifolds in terms of relative Gromov–Witten invariants of the toric compactifications. As a consequence, we obtain an equality between relative Gromov–Witten invariants and… read more here.
Keywords: toric calabi; calabi yau; relative gromov; gromov witten ... See more keywords
Enumerative geometry of surfaces and topological strings
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DOI: 10.1142/s0217751x23300089
Abstract: This survey covers recent developments on the geometry and physics of Looijenga pairs, namely pairs $(X,D)$ with $X$ a complex algebraic surface and $D$ a singular anticanonical divisor in it. I will describe a surprising… read more here.
Keywords: physics; geometry surfaces; geometry; witten invariants ... See more keywords
K-theoretic Gromov–Witten invariants of line degrees on flag varieties
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DOI: 10.1142/s0217751x24460138
Abstract: A homology class $d \in H_2(X)$ of a complex flag variety $X = G/P$ is called a line degree if the moduli space $\overline{M}_{0,0}(X,d)$ of 0-pointed stable maps to $X$ of degree $d$ is also… read more here.
Keywords: gromov witten; witten invariants; flag variety; line degrees ... See more keywords