Infinitesimal deformations of complements of plumbings of rational curves

Infinitesimal deformations of nodal stable curves

An analytic approach and description are presented for the moduli cotangent sheaf for suitable stable curve families including noded fibers. For sections of the square of the relative dualizing sheaf, the residue map at a node gives rise to an exact sequence. The residue kernel defines the vanishing residue subsheaf. For suitable stable curve families, the direct image sheaf on the base is locally free and the sequence of direct images is exact. Recent work of Hubbard-Koch and a formal argument provide that the direct image sheaf is naturally identified with the moduli cotangent sheaf. The res…

辛映射与锥形光滑中的球形对象

Symplectomorphisms and spherical objects in the conifold smoothing

研究了锥形光滑的辛映射群结构及锥形解析的球形对象分类，揭示了其无限生成性与三维仿射A₁情况下的分类结果。

On tangential deformations of homogeneous polynomials

The Jacobian ideal provides the set of infinitesimally trivial deformations for a homogeneous polynomial, or for the corresponding complex projective hypersurface. In this article, we investigate whether the associated linear deformation is indeed trivial, and show that the answer is no in a general situation. We also give a characterization of tangentially smoothable hypersurfaces with isolated singularities. Our results have applications in the local study of variations of projective hypersurfaces, complementing the global versions given by J. Carlson and P. Griffiths, R. Donagi and the auth…