Weighted-blowup correspondence of orbifold Gromov–Witten invariants and applications
Sign Up to like & getrecommendations! Published in 2019 at "Mathematische Annalen"
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 $$\mathsf… read more here.
Keywords: weighted blowup; blowup correspondence; gromov witten; mathsf ... See more keywords
Equivariant K-Theory and Refined Vafa–Witten Invariants
Sign Up to like & getrecommendations! Published in 2020 at "Communications in Mathematical Physics"
DOI: 10.1007/s00220-020-03821-1
Abstract: In Maulik and Thomas (in preparation) the Vafa–Witten theory of complex projective surfaces is lifted to oriented $${\mathbb {C}}^*$$ C ∗ -equivariant cohomology theories. Here we study the K-theoretic refinement. It gives rational functions in… read more here.
Keywords: vafa witten; refined vafa; equivariant theory; theory refined ... See more keywords
Smooth Invariants of Four-Dimensional Manifolds and Quantum Field Theory
Sign Up to like & getrecommendations! Published in 2020 at "Notices of the American Mathematical Society"
DOI: 10.1090/noti2000
Abstract: solutions to the Seiberg–Witten equations is much simpler than instanton moduli space (it is smooth and compact), it is easier to work with the Seiberg–Witten invariants. Happily, the Seiberg–Witten invariants turn out to be just… read more here.
Keywords: quantum field; seiberg witten; field; field theory ... See more keywords
Descendant log Gromov-Witten invariants for toric varieties and tropical curves
Sign Up to like & getrecommendations! Published in 2019 at "Transactions of the American Mathematical Society"
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
Sign Up to like & getrecommendations! Published in 2020 at "Transactions of the American Mathematical Society"
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
Sign Up to like & getrecommendations! Published in 2022 at "International Journal of Modern Physics A"
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