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Yujiro Kawamata

Publications and source records attributed to Yujiro Kawamata.

49 records · Page 3Linked to original sources
arXiv2002

D-equivalence and K-equivalence

Let $X$ and $Y$ be smooth projective varieties over $\mathbb{C}$. They are called {\it $D$-equivalent} if their derived categories of bounded complexes of coherent sheaves are equivalent as triangulated categories, while {\it $K$-equivalent} if they are birationally equivalent and the pull-backs of their canonical divisors to a common resolution coincide. We expect that the two equivalences coincide at least for birationally equivalent varieties. We shall provide a partial answer to the above problem in this paper.

math.AG↗
arXiv2001

Francia's flip and derived categories

We extend some of the results of Bondal-Orlov on the equivalence of derived categories to the case of orbifolds by using the category of coherent orbifold sheaves.

math.AG↗
arXiv2001

On algebraic fiber spaces

We construct a cohomological mixed Hodge complex on a fiber of a weakly semistable fibration using logarithmic de Rham complex.

math.AG↗
arXiv2000

On effective non-vanishing and base-point-freeness

Let $X$ be a complete normal variety, $B$ an effective $\mathbb{R}$-divisor on $X$, and $D$ a Cartier divisor on $X$. Assume that the pair $(X, B)$ is log terminal. We consider the problem whether $H^0(X, D) \ne 0$ and obtain some results in lower dimensions.

math.AG↗
arXiv1998

Index 1 covers of log terminal surface sigularities

We shall investigate index 1 covers of 2-dimensional log terminal singularities. The main result is that the index 1 cover is canonical if the characteristic of the base field is different from 2 or 3. We also give some counterexamples in the case of characteristic 2 or 3. By using this result, we correct an error in a previous paper.

math.AG↗
arXiv1997

Subadjunction of log canonical divisors II

We extend a subadjunction formula of log canonical divisors as in [K3] to the case when the codimension of the minimal center is arbitrary by using the positivity of the Hodge bundles.

alg-geom↗