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For an abelian tensor category a stack is constructed. As an application we show that our construction can be used to recover a quasi-compact separated scheme from the category of its quasi-coherent s...
Linear systems associated to unicuspidal rational plane curves
Linear systems associated unicuspidal rational plane curves
2012/2/29
A curve C in the projective plane is called non-negative if the self-intersection number of C after the minimal resolution of singularities of C is non-negative. Given a unicuspidal rational plane cur...
A canonical linear system associated to adjoint divisors in characteristic $p > 0$
Linear system test ideal multiplier ideal base-point-free ample characteristic p > 0
2011/9/15
Abstract: Suppose that $X$ is a projective variety over an algebraically closed field of characteristic $p > 0$. Further suppose that $L$ is an ample (or more generally in some sense positive) divisor...
Exceptional bundles associated to degenerations of surfaces
Exceptional bundles degenerations of surfaces Algebraic Geometry
2011/9/5
Abstract: In 1981 J. Wahl described smoothings of surface quotient singularities with no vanishing cycles. Given a smoothing of a projective surface X of this type, we construct an associated exceptio...
The Associated Map of the Nonabelian Gauss-Manin Connection
the Nonabelian Gauss-Manin Connection Algebraic Geometry The Associated Map
2011/9/1
Abstract: The Gauss-Manin connection for nonabelian cohomology spaces is the isomonodromy flow. We write down explicitly the vector fields of the isomonodromy flow and calculate its induced vector fie...
The Darboux coordinates for a new family of Hamiltonian operators and linearization of associated evolution equations
Hamiltonian operators bi-Hamiltonian systems evolution equations linearization
2010/12/28
A. de Sole, V. G. Kac, and M. Wakimoto have recently introduced a new family of compatible
Hamiltonian operators of the form H(N,0) = D2 ◦ ((1/u)◦D)2n ◦D, where N = 2n+3, n = 0, 1, ...