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Motivic Donaldson-Thomas invariants and McKay correspondence
Motivic Donaldson-Thomas invariants McKay correspondence Algebraic Geometry
2011/9/29
Abstract: Let $G\subset SL_2(C)\subset SL_3(C)$ be a finite group. We compute motivic Pandharipande-Thomas and Donaldson-Thomas invariants of the crepant resolution $Hilb^G(C^3)$ of $C^3/G$ generalizi...
A type of the Lefschetz hyperplane section theorem on \Q-Fano 3-folds with Picard number one and $1/2(1,1,1)$-singularities
Lefschetz hyperplane section theorem Algebraic Geometry
2011/9/23
Abstract: We prove a type of the Lefschetz hyperplane section theorem on Q-Fano 3-folds with Picard number one and $1/2(1,1,1)$-singularities by using some degeneration method. As a byproduct, we obta...
Non-commutative Hodge structures
Non-commutative Hodge structure Fourier-Laplace transformation Brieskorn lattice
2011/9/23
Abstract: This article gives a survey of recent results on a generalization of the notion of a Hodge structure. The main example is related to the Fourier-Laplace transform of a variation of polarizab...
Bergman Type Metrics in Tower of Coverings
Bergman Type Metrics Tower of Coverings Algebraic Geometry
2011/9/22
Abstract: We establish a version of a statement attributed to Kazhdan by Yau. As a corollary, we obtain a more transparent form of our uniformization theorem in complex algebraic geometry.
Hidden Hodge symmetries and Hodge correlators
Hidden Hodge symmetries Hodge correlators Algebraic Geometry
2011/9/22
Abstract: The Hodge Galois group is the Tannakian Galois group of the category of real mixed Hodge structures. It has a subgroup, called the twistor Galois group, which is the Galois group of the cate...
A note on Griffiths infinitesimal invariant for curves
Griffiths infinitesimal invariant curves Algebraic Geometry
2011/9/22
Abstract: Given a generic curve of genus $g\geqslant4$ and a smooth point $L\in W_{g-1}^{1}(C)$, whose linear system is base-point free, we consider the Abel-Jacobi normal function associated to $L^{\...
On a canonical class of Green currents for the unit sections of abelian schemes
unit sections of abelian schemes canonical class of Green currents Algebraic Geometry
2011/9/22
Abstract: We show that on any abelian scheme over a complex quasi-projective smooth variety, there is a Green current for the zero-section, which is axiomatically determined up to $\partial$ and $\bar...
Resolution except for minimal singularities II. The case of four variables
birational geometry resolution of singularities normal crossings desingularization invariant normal form
2011/9/22
Abstract: In this sequel to Resolution except for minimal singularities I, we find the smallest class of singularities in four variables with which we necessarily end up if we resolve singularities ex...
Resolution except for minimal singularities I
birational geometry resolution of singularities normal crossings desingularization invariant normal form
2011/9/22
Abstract: The philosophy of the article is that the desingularization invariant together with natural geometric information can be used to compute local normal forms of singularities. The idea is used...
Abstract: We show that the dimer model on a bipartite graph on a torus gives rise to a quantum integrable system of special type - a cluster integrable system. The phase space of the classical system ...
Orbifold Euler characteristics for dual invertible polynomials
Orbifold Euler characteristics dual invertible polynomials Algebraic Geometry
2011/9/22
Abstract: To construct mirror symmetric Landau-Ginzburg models, P.Berglund, T.H\"ubsch and M.Henningson considered a pair $(f,G)$ consisting of an invertible polynomial $f$ and an abelian group $G$ of...
The canonical ring of a 3-connected curve
algebraic curve Noether’s theorem canonical ring
2011/9/22
Abstract: Let C be a Gorenstein curve which is either reduced or contained in a smooth algebraic surface. We show that the canonical ring R(C, \omega_C)=\oplus_{k \geq 0} H^0(C, \omega_C^k) is generat...
Beauville surfaces, moduli spaces and finite groups
Beauville surfaces moduli spaces finite groups Algebraic Geometry
2011/9/22
Abstract: In this paper we give the asymptotic growth of the number of connected components of the moduli space of surfaces of general type corresponding to certain families of Beauville surfaces with...
Using Tropical Degenerations For Proving The Nonexistence Of Certain Nets
Tropical Degenerations The Nonexistence Of Certain Nets Algebraic Geometry
2011/9/22
Abstract: A net is a special configuration of lines and points in the projective plane. There are certain restrictions on the number of its lines and points. We proved that there cannot be any (4,4) n...
$sl_2$ conformal block divisors and the nef cone of $\bar{M}_{0,n}$
the nef cone Algebraic Geometry
2011/9/21
Abstract: We show that $sl_2$ conformal block divisors do not cover the nef cone of $\bar{M}_{0,6}$, or the $S_9$-invariant nef cone of $\bar{M}_{0,9}$. A key point is to relate the nonvanishing of in...