1,721,049 research outputs found
Nodal surfaces with obstructed deformations
Full text linkIn this text we show that the deformation space of a nodal surface of degree is smooth and of the expected dimension if or and has at most nodes. (The case was previously covered by Alexandru Dimca by using different techniques.)
For we give explicit examples of nodal surfaces with nodes, for which the tangent space to the deformation space has larger dimension than expected.
We give a short discussion on the shape of the deformation space of surfaces of the form , where is a linear form.v2: Added a reference to a similar result by Alexandru Dimca and a discussion on the difference between Dimca\u27s result and ours v3: Expanded several argument
On the syzygies and Hodge theory of nodal hypersurfaces
No full textv3. Some applications to the deformation theory of nodal surfaces in are addedWe give sharp lower bounds for the degree of the syzygies involving the partial derivatives of a homogeneous polynomial defining an even dimensional nodal hypersurface. This implies the validity of formulas due to M. Saito, L. Wotzlaw and the author for the graded pieces with respect to the Hodge filtration of the top cohomology of the hypersurface complement in many new cases. A classical result by Severi on the position of the singularities of a nodal surface in is improved and applications to deformation theory of nodal surfaces are given
Variance of the spectral numbers and Newton polygons
No full textAbstractUsing the theory of the mixed Hodge structure one can define a notion of spectrum of a singularity or of a polynomial. Recently Claus Hertling proposed a conjecture about the variance of the spectrum of a singularity. Alexandru Dimca proposed a similar conjecture on polynomials. Here, we prove these two conjectures in the case of dimension 2 and when the singularity or the polynomial is Newton non-degenerated and commode
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