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