20 citations · 56 across the 9 of their papers we have counts for
15 papers
Gromov--Witten invariants with naive tangency conditions
Felix Janda, Tony Yue Yu
We introduce Gromov-Witten invariants with naive tangency conditions at the marked points of the source curve. We then establish an explicit formula which expresses Gromov-Witten i…
Secondary fan, theta functions and moduli of Calabi-Yau pairs
Paul Hacking, Sean Keel, Tony Yue Yu
We conjecture that any connected component of the moduli space of triples where is a smooth projective variety, is a normal crossing anti-canoni…
Non-archimedean quantum K-invariants
Mauro Porta, Tony Yue Yu
We construct quantum K-invariants in non-archimedean analytic geometry. Contrary to the classical approach in algebraic geometry via perfect obstruction theory, we build on our pre…
The Frobenius structure theorem for affine log Calabi-Yau varieties containing a torus
Sean Keel, Tony Yue Yu
Let be an affine log Calabi-Yau variety containing an open algebraic torus. We show that the naive counts of rational curves in uniquely determine a commutative associative…
The non-archimedean SYZ fibration
Johannes Nicaise, Chenyang Xu, Tony Yue Yu
We construct non-archimedean SYZ fibrations for maximally degenerate Calabi-Yau varieties, and we show that they are affinoid torus fibrations away from a codimension two subset of…
Derived Hom spaces in rigid analytic geometry
Mauro Porta, Tony Yue Yu
We construct a derived enhancement of Hom spaces between rigid analytic spaces. It encodes the hidden deformation-theoretic informations of the underlying classical moduli space. T…
Representability theorem in derived analytic geometry
Mauro Porta, Tony Yue Yu
We prove the representability theorem in derived analytic geometry. The theorem asserts that an analytic moduli functor is a derived analytic stack if and only if it is compatible…
Enumeration of holomorphic cylinders in log Calabi-Yau surfaces. II. Positivity, integrality and the gluing formula
Tony Yue Yu
We prove three fundamental properties of counting holomorphic cylinders in log Calabi-Yau surfaces: positivity, integrality and the gluing formula. Positivity and integrality asser…
Derived non-archimedean analytic spaces
Mauro Porta, Tony Yue Yu
We propose a derived version of non-archimedean analytic geometry. Intuitively, a derived non-archimedean analytic space consists of an ordinary non-archimedean analytic space equi…
Enumeration of holomorphic cylinders in log Calabi-Yau surfaces. I
Tony Yue Yu
We define the counting of holomorphic cylinders in log Calabi-Yau surfaces. Although we start with a complex log Calabi-Yau surface, the counting is achieved by applying methods fr…
Higher analytic stacks and GAGA theorems
Mauro Porta, Tony Yue Yu
We develop the foundations of higher geometric stacks in complex analytic geometry and in non-archimedean analytic geometry. We study coherent sheaves and prove the analog of Graue…
Tropicalization of the moduli space of stable maps
Tony Yue Yu
Let be an algebraic variety and let be a tropical variety associated to . We study the tropicalization map from the moduli space of stable maps into to the moduli sp…
Gromov compactness in non-archimedean analytic geometry
Tony Yue Yu
Gromov's compactness theorem for pseudo-holomorphic curves is a foundational result in symplectic geometry. It controls the compactness of the moduli space of pseudo-holomorphic cu…
The number of vertices of a tropical curve is bounded by its area
Tony Yue Yu
We introduce the notion of tropical area of a tropical curve defined in an open subset of . We prove that the number of vertices of a tropical curve is bounded by the…
Balancing conditions in global tropical geometry
Tony Yue Yu
We study tropical geometry in the global setting using Berkovich's deformation retraction. We state and prove the generalized balancing conditions in this setting. Starting with a…