1,721,014 research outputs found
General curves on algebraic surfaces
No full textWe give upper bounds on the genus of a curve with general moduli assuming that it can be embedded in a projective nonsingular surface so that . We find such bounds for all types of surfaces of intermediate Kodaira dimension and, under mild restrictions, for surfaces of general type whose minimal model satisfies the Castelnuovo inequality K_Z^2 \ge 3\chi(\O_Z) - 10. In this last case we obtain . In the other cases considered the bounds are lower
Some remarks on Riemann's existence theorem
No full textInvited conference at the international meeting 'Algebraic curves, monodromy and related topics', Politecnico di Milano. April 2004.(web page:http://www.mate.polimi.it/cm
Deformations of Algebraic Schemes
No full textPresents an account of deformation theory in classical algebraic geometry that brings together some results scattered in the literature. This book includes applications to the construction and properties of Severi varieties of families of plane nodal curves, space curves, deformations of quotient singularities, local Picard functors, and more
The local cohomology of the jacobian ring
No full textWe study the 0-th local cohomology module of the jacobian ring of a singular reduced complex projective hypersurface X, by relating it to the sheaf of logarithmic vector field along X. We investigate the analogies between the local cohomology and the well known properties of the jacobian ring of a nonsingular hypersurface. In particular we study self-duality, Hodge theoretic and Torelli type questions
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