Q-gorenstein Deformations of Nonnormal Surfaces
نویسنده
چکیده
Let ∆ ⊂ H be the germ of a non-normal surface along a proper curve with smooth components such that the high index points of H are semilog-terminal and the Gorenstein singular points are semi-log-canonical. We describe the sheaf T 1 qG(H) of Q-Gorenstein deformations of H, we show that T 1 qG(H)/(torsion) is a line bundle L on ∆ and we calculate the degree of the restriction of L on every irreducible component of ∆. Finally we obtain criteria for ∆ ⊂ H to have Q-Gorenstein terminal smoothings.
منابع مشابه
Toric I Q-gorenstein Singularities
For an affine, toric I Q-Gorenstein variety Y (given by a lattice polytope Q) the vector space T 1 of infinitesimal deformations is related to the complexified vector spaces of rational Minkowski summands of faces of Q. Moreover, assuming Y to be an isolated, at least 3-dimensional singularity, Y will be rigid unless it is even Gorenstein and dimY = 3 (dimQ = 2). For this particular case, so-ca...
متن کاملCanonical Symplectic Structures and Deformations of Algebraic Surfaces
We show that a minimal surface of general type has a canonical symplectic structure (unique up to symplectomorphism) which is invariant for smooth deformation. Our main theorem is that the symplectomorphism type is also invariant for deformations which allow certain normal singular-ities, called Single Smoothing Singularities (and abbreviated as SSS), and moreover for deformations yielding Q-Go...
متن کاملSmoothings of Schemes with Non-isolated Singularities
In this paper we study the deformation and Q-Gorenstein deformation theory of schemes with non-isolated 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 Q-Gorenstein smoothings.
متن کاملOn Gorenstein surfaces dominated by P 2
In this paper we prove that a normal Gorenstein surface dominated by P 2 is isomorphic to a quotient P 2 /G, where G is a finite group of automorphisms of P 2 (except possibly for one surface V ′ 8). We can completely classify all such quotients. Some natural conjectures when the surface is not Gorenstein are also stated.
متن کاملSymplectic structures of algebraic surfaces and deformation
We show that a surface of general type has a canonical symplectic structure (up to symplectomorphism) which is invariant for smooth deformation. Our main theorem is that the symplectomorphism type is also invariant for deformations which also allow certain normal singularities, called Single Smoothing Singularities ( and abbreviated as SSS), or yielding Q-Gorenstein smoothings of quotient singu...
متن کامل