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SMOOTHINGS OF SCHEMES WITH NONISOLATED SINGULARITIES
, 2009
"... In this paper we study the deformation and QGorenstein deformation theory of schemes with nonisolated singularities. We obtain obstruction spaces for the existence of deformations and also for local deformations to exist globally. Finally we obtain explicit criteria in order for a pure and reduced ..."
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In this paper we study the deformation and QGorenstein deformation theory of schemes with nonisolated singularities. We obtain obstruction spaces for the existence of deformations and also for local deformations to exist globally. Finally we obtain explicit criteria in order for a pure and reduced scheme of finite type over a field k to have smoothings and QGorenstein smoothings.
TORIC DEGENERATIONS OF GIT QUOTIENTS, CHOW QUOTIENTS, AND M0,N
, 2006
"... The moduli space M0,n plays important roles in algebraic geometry and theoretical physics. Yet, some basic properties of M0,n still remain open. For example, M0,n is rational and nearly toric (that is, it contains a toric variety as a Zariski open subset), but it is not a toric variety itself starti ..."
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The moduli space M0,n plays important roles in algebraic geometry and theoretical physics. Yet, some basic properties of M0,n still remain open. For example, M0,n is rational and nearly toric (that is, it contains a toric variety as a Zariski open subset), but it is not a toric variety itself starting
A Generalization of Voronoi's . . .
, 2007
"... We consider Voronoi’s reduction theory of positive definite quadratic forms which is based on Delone subdivision. We extend it to forms and Delone subdivisions having a prescribed symmetry group. Even more general, the theory is developed for forms which are restricted to a linear subspace in the sp ..."
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We consider Voronoi’s reduction theory of positive definite quadratic forms which is based on Delone subdivision. We extend it to forms and Delone subdivisions having a prescribed symmetry group. Even more general, the theory is developed for forms which are restricted to a linear subspace in the space of quadratic forms. We apply the new theory to complete the classification of totally real thin algebraic number fields which was recently initiated by BayerFluckiger and Nebe. Moreover,
LOGCANONICAL PAIRS AND GORENSTEIN STABLE SURFACES WITH K2X = 1
"... Abstract. We classify logcanonical pairs (X,∆) of dimension two with KX+∆ an ample Cartier divisor with (KX + ∆)2 = 1, giving some applications to stable surfaces with K2 = 1. A rough classification is also given in the case ∆ = 0. Contents ..."
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Abstract. We classify logcanonical pairs (X,∆) of dimension two with KX+∆ an ample Cartier divisor with (KX + ∆)2 = 1, giving some applications to stable surfaces with K2 = 1. A rough classification is also given in the case ∆ = 0. Contents