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43
Stable twisted curves and their rspin structures
, 2007
"... The object of this paper is the notion of rspin structure: a line bundle whose rth power is isomorphic to the canonical bundle. Over the moduli functor Mg of smooth genusg curves, rspin structures form a finite torsor under the group of rtorsion line bundles. Over the moduli functor Mg of stable ..."
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Cited by 21 (7 self)
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The object of this paper is the notion of rspin structure: a line bundle whose rth power is isomorphic to the canonical bundle. Over the moduli functor Mg of smooth genusg curves, rspin structures form a finite torsor under the group of rtorsion line bundles. Over the moduli functor Mg of stable curves, rspin structures form an étale stack, but the finiteness and the torsor structure are lost. In the present work, we show how this bad picture can be definitely improved simply by placing the problem in the category of Abramovich and Vistoli’s twisted curves. First, we find that within such category there exist several different compactifications of Mg; each one corresponds to a different multiindex ⃗ l = (l0, l1,...) identifying a notion of stability: ⃗ lstability. Then, we determine the suitable choices of ⃗ l for which rspin structures form a finite torsor over the moduli of ⃗ lstable curves.
LG/CY CORRESPONDENCE: THE STATE SPACE ISOMORPHISM
, 908
"... Abstract. We provide a degreepreserving isomorphism between the cohomology of finite quotients of Calabi–Yau hypersurfaces inside a weighted projective space and the Fan–Jarvis–Ruan–Witten state space of the associated Landau–Ginzburg singularity theory. This fulfills the physical conjectural state ..."
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Cited by 18 (1 self)
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Abstract. We provide a degreepreserving isomorphism between the cohomology of finite quotients of Calabi–Yau hypersurfaces inside a weighted projective space and the Fan–Jarvis–Ruan–Witten state space of the associated Landau–Ginzburg singularity theory. This fulfills the physical conjectural statement of Landau– Ginzburg/Calabi–Yau correspondence for group actions contained in the special linear group and extends it beyond. In the case of “invertible ” singularities, via a recent result of Krawitz, this yields a proof of a classical mirror symmetry conjecture for the mirror pairs constructed by Berglund, Hübsch, and Krawitz. This technique applies beyond the classical Batyrev and Borisov’s theorem which requires the ambient weighted projective space to be Gorenstein. 1.
Identification of the Givental formula with the spectral curve topological recursion procedure
 Comm. Math. Phys
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Yefeng: LandauGinzburg/CalabiYau Correspondence of all Genera for Elliptic Orbifold P1
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BCOV theory via Givental group action on . . .
, 2008
"... In a previous paper, Losev, me, and Shneiberg constructed a full descendant potential associated to an arbitrary cyclic Hodge dGBV algebra. This contruction extended the construction of Barannikov and Kontsevich of solution of the WDVV equation, based on the earlier paper of Bershadsky, Cecotti, O ..."
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Cited by 13 (6 self)
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In a previous paper, Losev, me, and Shneiberg constructed a full descendant potential associated to an arbitrary cyclic Hodge dGBV algebra. This contruction extended the construction of Barannikov and Kontsevich of solution of the WDVV equation, based on the earlier paper of Bershadsky, Cecotti, Ooguri, and Vafa. In the present paper, we give an interpretation of this full descendant potential in terms of Givental group action on cohomological field theories. In particular, the fact that it satisfies all
On the geometry of the moduli space of spin curves
"... Abstract. We determine the smooth locus and the locus of canonical singularities in the Cornalba compactification Sg of the moduli space Sg of spin curves, i.e., smooth curves of genus g with a theta characteristic. Moreover, the following lifting result for pluricanonical forms is proved: Every plu ..."
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Cited by 11 (0 self)
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Abstract. We determine the smooth locus and the locus of canonical singularities in the Cornalba compactification Sg of the moduli space Sg of spin curves, i.e., smooth curves of genus g with a theta characteristic. Moreover, the following lifting result for pluricanonical forms is proved: Every pluricanonical form on the smooth locus of Sg extends holomorphically to a desingularisation of Sg. 1.
Wconstraints for the total descendant potential of a simple singularity
 Compositio Math
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Polynomiality of hurwitz numbers, bouchardmario conjecture, and a new proof of the elsv formula. arXiv:1307.4729
, 2013
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Notes on axiomatic Gromov–Witten theory and applications
"... The purpose of these notes is to give their readers some idea of Givental’s axiomatic Gromov–Witten theory, and a few applications. Due to the scope of these notes, some statements are not precisely formulated and almost all proofs are omitted. However, we try to ..."
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Cited by 7 (4 self)
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The purpose of these notes is to give their readers some idea of Givental’s axiomatic Gromov–Witten theory, and a few applications. Due to the scope of these notes, some statements are not precisely formulated and almost all proofs are omitted. However, we try to