Results 1 to 10 of about 160 (40)

Convergence of the mirror to a rational elliptic surface

Transactions of the London Mathematical Society, 2021
The construction introduced by Gross, Hacking and Keel in (Several Complex Variables (Springer, New York, NY, 1976))allows one to construct a formal mirror family to a pair (S,D) where S is a smooth rational projective surface and D a certain type of ...
Lawrence Jack Barrott
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Mirror symmetry for Nahm branes [PDF]

Épijournal de Géométrie Algébrique, 2022
The Dirac--Higgs bundle is a hyperholomorphic bundle over the moduli space of stable Higgs bundles of coprime rank and degree. We provide an algebraic generalization to the case of trivial degree and the rank higher than $1$.
Emilio Franco, Marcos Jardim
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The Mori fan of the Dolgachev-Nikulin-Voisin family in genus $2$ [PDF]

Épijournal de Géométrie Algébrique, 2022
In this paper we study the Mori fan of the Dolgachev-Nikulin-Voisin family in degree $2$ as well as the associated secondary fan. The main result is an enumeration of all maximal dimensional cones of the two fans.
Klaus Hulek, Carsten Liese
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On genus one mirror symmetry in higher dimensions and the BCOV conjectures

Forum of Mathematics, Pi, 2022
The mathematical physicists Bershadsky–Cecotti–Ooguri–Vafa (BCOV) proposed, in a seminal article from 1994, a conjecture extending genus zero mirror symmetry to higher genera.
Dennis Eriksson, Gerard Freixas i Montplet, Christophe Mourougane   +2 more
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Decompositions of moduli spaces of vector bundles and graph potentials

Forum of Mathematics, Sigma, 2023
We propose a conjectural semiorthogonal decomposition for the derived category of the moduli space of stable rank 2 bundles with fixed determinant of odd degree, independently formulated by Narasimhan. We discuss some evidence for and furthermore propose
Pieter Belmans, Sergey Galkin, Swarnava Mukhopadhyay   +2 more
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Analytic continuation of better-behaved GKZ systems and Fourier-Mukai transforms [PDF]

Épijournal de Géométrie Algébrique
We study the relationship between solutions to better-behaved GKZ hypergeometric systems near different large radius limit points, and their geometric counterparts given by the $K$-groups of the associated toric Deligne-Mumford stacks. We prove that the $
Zengrui Han
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A mirror theorem for Gromov-Witten theory without convexity

Forum of Mathematics, Sigma
We prove a genus zero Givental-style mirror theorem for all complete intersections in toric Deligne-Mumford stacks, which provides an explicit slice called big I-function on Givental’s Lagrangian cone for such targets.
Jun Wang
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Family Floer mirror space for local SYZ singularities

Forum of Mathematics, Sigma
We give a mathematically precise statement of the SYZ conjecture between mirror space pairs and prove it for any toric Calabi-Yau manifold with the Gross Lagrangian fibration. To date, it is the first time we realize the SYZ proposal with singular fibers
Hang Yuan
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Semistable degenerations of Calabi–Yau manifolds and mirror P=W conjectures

Forum of Mathematics, Sigma
Mirror symmetry for a semistable degeneration of a Calabi–Yau manifold was first investigated by Doran–Harder–Thompson when the degenerate fiber is a union of two quasi-Fano manifolds.
Sukjoo Lee
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The KSBA moduli space of stable log Calabi–Yau surfaces

Forum of Mathematics, Pi
We prove that every irreducible component of the coarse Kollár-Shepherd-Barron and Alexeev (KSBA) moduli space of stable log Calabi–Yau surfaces admits a finite cover by a projective toric variety. This verifies a conjecture of Hacking–Keel–Yu. The proof
Valery Alexeev, Hulya Arguz, Pierrick Bousseau   +2 more
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