Minimal discrepancies of hypersurface singularities
We give an upper bound for the minimal discrepancies of hypersurface singularities. As an application, we show that Shokurov's conjecture is true for log-terminal threefolds.
alg-geom↗
arXiv subjects
Vladimir Masek
Publications and source records attributed to Vladimir Masek.
Kawachi's invariant for normal surface singularities
We study a useful numerical invariant of normal surface singularities, introduced recently by T. Kawachi. Using this invariant, we give a quick proof of the (well-known) fact that all log-canonical surface singularities are either elliptic Gorenstein or rational (without assuming a priori that they are Q-Gorenstein). The main result is a criterion (stated in terms of Kawachi's invariant) regarding global generation of adjoint linear systems on normal surfaces with boundary. Such results can be used in proving effective estimates for global generation on singular threefolds. The theorem of Ein-Lazarsfeld and Kawamata, which says that the minimal center of log-canonical singularities is always normal, explains why the results proved here are relevant in that situation.
alg-geom↗
Very ampleness of adjoint linear systems on smooth surfaces with boundary
Let M be a Q-divisor on a smooth surface over C. In this paper we give criteria for very ampleness of the adjoint of the round-up of M. (Similar results for global generation were given by Ein and Lazarsfeld and used in their proof of Fujita's Conjecture in dimension 3.) In the last section we discuss an example which suggests that this kind of criteria might also be useful in the study of linear systems on surfaces.
alg-geom↗