8 research outputs found
Counting divisorial contractions with centre a -singularity
First, we simplify the existing classification due to Kawakita and Yamamoto
of 3-dimensional divisorial contractions with centre a -singularity.
Next, we consider divisorial contractions of discrepancy at least 2 to a fixed
variety with centre a -singularity. We show that if there exists one such
divisorial contraction, then there exist uncountably many such divisorial
contractions.Comment: 16 page
Del Pezzo surfaces in weighted projective spaces
We study singular del Pezzo surfaces that are quasi-smooth and well-formed weighted hypersurfaces. We give an algorithm how to classify all of them
Log canonical thresholds of high multiplicity reduced plane curves
We compute log canonical thresholds of reduced plane curves of degree at
points of multiplicity . As a consequence, we describe all possible values
of log canonical threshold that are less than for reduced plane
curves of degree . In addition, we compute log canonical thresholds for all
reduced plane curves of degree less than 6.Comment: 13 page
Blowups of smooth Fano hypersurfaces, their birational geometry and divisorial stability
Let be a smooth -dimensional hypersurface in
and a smooth -dimensional Fano hypersurface in where and . Let be the blowup of
along . We give a constructive proof that is a Mori dream
space. In particular, we describe its Mori chamber decomposition and the
associated birational models of . We classify for which and the
variety is a Fano manifold and we initiate the study of K-stability of .Comment: 20 page
Birational geometry of sextic double solids with a compound singularity
Sextic double solids, double covers of branched along a sextic surface, are the lowest degree Gorenstein Fano 3-folds, hence are expected to behave very rigidly in terms of birational geometry. Smooth sextic double solids, and those which are -factorial with ordinary double points, are known to be birationally rigid. In this article, we study sextic double solids with an isolated compound singularity. We prove a sharp bound , describe models for each explicitly and prove that sextic double solids with are birationally non-rigid
Birational models of terminal sextic double solids
We study sextic double solids, which are double covers of ℙ^3 branched along a sextic surface. We impose that such a 3-fold carries an isolated compound A_n singularity, abbreviated by cA_n. We first prove the bound n ≤ 8 for having an isolated cA_n singularity. We then explicitly parametrize sextic double solids with an isolated cA_n singularity and show that general sextic double solids with a cA_n point with n ≥ 4 are birationally non-rigid viewed as Mori fibre spaces. Birational non-rigidity is shown by constructing Sarkisov links starting with an extremal divisorial extraction from the singular point in each case