Results 1 to 10 of about 62 (61)
, 2012 Object of study in this paper are the Hurwitz numbers. They were introduced by Hurwitz in the end of nineteenth century and still they are of great interest. The Hurwitz numbers are important in topology because they enumerate ramified coverings of two-dimensional surfaces, but not only.
VETRO, Francesca
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Forum of Mathematics, Pi, 2021 We prove a higher genus version of the genus $0$ local-relative correspondence of van Garrel-Graber-Ruddat: for $(X,D)$ a pair with X a smooth projective variety and D a nef smooth divisor, maximal contact Gromov-Witten theory of $(X,D)$ with $\lambda _g$
Pierrick Bousseau +3 more
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Rational cuspidal curves in a moving family of ℙ2
Complex Manifolds, 2021 In this paper we obtain a formula for the number of rational degree d curves in ℙ3 having a cusp, whose image lies in a ℙ2 and that passes through r lines and s points (where r + 2s = 3d + 1).
Mukherjee Ritwik, Singh Rahul Kumar
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Crepant resolutions and open strings II [PDF]
Épijournal de Géométrie Algébrique, 2018 We recently formulated a number of Crepant Resolution Conjectures (CRC) for open Gromov-Witten invariants of Aganagic-Vafa Lagrangian branes and verified them for the family of threefold type A-singularities. In this paper we enlarge the body of evidence
Andrea Brini, Renzo Cavalieri
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Quasimaps to GIT fibre bundles and applications
Forum of Mathematics, Sigma, 2021 In [4], Brown proved that the I-function of a toric fibration lies on the overruled Lagrangian cone of its $g=0$ Gromov–Witten theory, introduced by Coates and Givental [8]. In this paper, we prove the theorem for partial flag-variety fibrations.
Jeongseok Oh
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Forum of Mathematics, Sigma, 2021 We prove an equivalence between the Bryan-Steinberg theory of $\pi $-stable pairs on $Y = \mathcal {A}_{m-1} \times \mathbb {C}$ and the theory of quasimaps to $X = \text{Hilb}(\mathcal {A}_{m-1})$, in the form of an equality of K-theoretic equivariant
Henry Liu
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Curves on K3 surfaces in divisibility 2
Forum of Mathematics, Sigma, 2021 We prove a conjecture of Maulik, Pandharipande and Thomas expressing the Gromov–Witten invariants of K3 surfaces for divisibility 2 curve classes in all genera in terms of weakly holomorphic quasi-modular forms of level 2.
Younghan Bae, Tim-Henrik Buelles
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Extremal Gromov-Witten invariants of the Hilbert scheme of $3$ Points
Forum of Mathematics, Sigma, 2023 We determine all the extremal Gromov-Witten invariants of the Hilbert scheme of $3$ points on a smooth projective complex surface. Our result for the genus- $1$ case verifies a conjecture that we propose for the genus- $1$ extremal ...
Jianxun Hu, Zhenbo Qin
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Higher rank K-theoretic Donaldson-Thomas Theory of points
Forum of Mathematics, Sigma, 2021 We exploit the critical structure on the Quot scheme $\text {Quot}_{{{\mathbb {A}}}^3}({\mathscr {O}}^{\oplus r}\!,n)$, in particular the associated symmetric obstruction theory, in order to study rank r K-theoretic Donaldson-Thomas (DT) invariants of ...
Nadir Fasola +2 more
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Virasoro constraints for stable pairs on toric threefolds
Forum of Mathematics, Pi, 2022 Using new explicit formulas for the stationary Gromov–Witten/Pandharipande–Thomas ( $\mathrm {GW}/{\mathrm {PT}}$ ) descendent correspondence for nonsingular projective toric threefolds, we show that the correspondence intertwines the Virasoro ...
Miguel Moreira +3 more
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