27 citations · 44 across the 16 of their papers we have counts for
18 papers
K-stability of Fano weighted hypersurfaces via plt flags and convex geometry
Livia Campo, Kento Fujita, Taro Sano +1
We develop a framework to study the K-stability of weighted Fano hypersurfaces based on a combination of birational and convex-geometric techniques. As an application, we prove tha…
Delta invariants of weighted hypersurfaces
Taro Sano, Luca Tasin
We give a lower bound for the delta invariant of the fundamental divisor of a quasi-smooth weighted hypersurface. As a consequence, we prove K-stability of a large class of quasi-s…
On Hodge structures of compact complex manifolds with semistable degenerations
Taro Sano
Compact Kähler manifolds satisfy several nice Hodge-theoretic properties such as the Hodge symmetry, the Hard Lefschetz property and the Hodge-Riemann bilinear relations, etc. In t…
Construction of non-Kähler Calabi-Yau manifolds by log deformations
Taro Sano
We survey recent construction of non-Kähler Calabi-Yau manifolds by smoothing SNC varieties obtained by non-trivial isomorphisms of strict Calabi-Yau manifolds. We also give a new…
Infinitely many families of Sasaki-Einstein metrics on spheres
Yuchen Liu, Taro Sano, Luca Tasin
We show that there exist infinitely many families of Sasaki-Einstein metrics on every odd-dimensional standard sphere of dimension at least . We also show that the same result i…
On K-stability of Fano weighted hypersurfaces
Taro Sano, Luca Tasin
Let be a quasi-smooth weighted Fano hypersurface of degree and index such that for all , with .…
Examples of non-Kähler Calabi-Yau manifolds with arbitrarily large
Taro Sano
We construct non-Kähler Calabi-Yau manifolds of dimension 4 with arbitrarily large 2nd Betti numbers by smoothing normal crossing varieties. The examples have K3 fibrations…
On birational boundedness of some Calabi-Yau hypersurfaces
Taro Sano
We show the birational boundedness of anti-canonical irreducible hypersurfaces which form 3-fold plt pairs. We also treat a collection of Du Val K3 surfaces which is birationally b…
Examples of non-Kähler Calabi-Yau 3-folds with arbitrarily large
Kenji Hashimoto, Taro Sano
We construct non-Kähler simply connected Calabi-Yau 3-folds with arbitrarily large 2nd Betti numbers by smoothing normal crossing varieties with trivial dualizing sheaves.
Effective non-vanishing for Fano weighted complete intersections
Marco Pizzato, Taro Sano, Luca Tasin
We show that Ambro-Kawamata's non-vanishing conjecture holds true for a quasi-smooth WCI X which is Fano or Calabi-Yau, i.e. we prove that, if H is an ample Cartier divisor on X, t…
Smoothing cones over K3 surfaces
Stephen Coughlan, Taro Sano
We prove that the affine cone over a general primitively polarised K3 surface of genus g is smoothable if and only if g\le 10 or g=12. We also give several examples of singularitie…
Deformations of weak -Fano 3-folds
Taro Sano
We prove that a weak -Fano -fold with terminal singularities has unobstructed deformations. By using this result and computing some invariants of a terminal singular…
Noncommutative rigidity of the moduli stack of stable pointed curves
Shinnosuke Okawa, Taro Sano
We prove that the second Hochschild cohomology group of the moduli stack of stable -pointed genus curves vanishes for all but finitely many .
Deforming elephants of Q-Fano threefolds
Taro Sano
We study deformations of a pair of a -Fano -fold with only terminal singularities and its elephant . We prove that, if there exists $D \in |{-}K_…
On deformations of Q-Fano threefolds II
Taro Sano
We investigate some coboundary map associated to a -dimensional terminal singularity which is important in the study of deformations of singular -folds. We prove that this ma…
Unobstructedness of deformations of weak Fano manifolds
Taro Sano
We prove that a weak Fano manifold has unobstructed deformations. For a general variety, we investigate conditions under which a variety is necessarily obstructed.
On deformations of Q-Fano threefolds
Taro Sano
We study the deformation theory of a Q-Fano 3-fold with only terminal singularities. First, we show that the Kuranishi space of a Q-Fano 3-fold is smooth. Second, we show that ever…
Seshadri constants on rational surfaces with anticanonical pencils
Taro Sano
We study a Seshadri constant at a general point on a rational surface whose anticanonical linear system contains a pencil. First, we describe a Seshadri constant of an ample line b…