175 research outputs found
Obstructions to the Existence of Sasaki-Einstein Metrics
We describe two simple obstructions to the existence of Ricci-flat Kahler
cone metrics on isolated Gorenstein singularities or, equivalently, to the
existence of Sasaki-Einstein metrics on the links of these singularities. In
particular, this also leads to new obstructions for Kahler-Einstein metrics on
Fano orbifolds. We present several families of hypersurface singularities that
are obstructed, including 3-fold and 4-fold singularities of ADE type that have
been studied previously in the physics literature. We show that the AdS/CFT
dual of one obstruction is that the R-charge of a gauge invariant chiral
primary operator violates the unitarity bound.Comment: 35 pages, 1 figure; references and a footnote adde
Classification of elliptic and K3 fibrations birational to some Q-Fano 3-folds
A complete classification is presented of elliptic and K3 fibrations
birational to certain mildly singular complex Fano 3-folds. Detailed proofs are
given for one example case, namely that of a general hypersurface X of degree
30 in weighted P^4 with weights 1,4,5,6,15; but our methods apply more
generally. For constructing birational maps from X to elliptic and K3
fibrations we use Kawamata blowups and Mori theory to compute anticanonical
rings; to exclude other possible fibrations we make a close examination of the
strictly canonical singularities of (X,(1/n)H), where H is the linear system
associated to the putative birational map and n is its anticanonical degree.Comment: 24 page
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