• Corpus ID: 13299117

HIGHER DIMENSIONAL ALGEBRAIC GEOMETRY

@inproceedings{Yuzawa2006HIGHERDA,
  title={HIGHER DIMENSIONAL ALGEBRAIC GEOMETRY},
  author={Echigo Yuzawa and Shigeharu Takayama and Osamu Fujino and Takehiko Yasuda and Dan Abramovich and Yoshinori Namikawa and Jarosław Włodarczyk},
  year={2006}
}
I will talk about termination of flips in dimension 4 following AHacon-Kawamata and the work of Shokurov since then. 
faculty.ms.u-tokyo.ac.jp
254 Citations
Highly Influential Citations
6
Background Citations
33
Methods Citations
8

254 Citations

Citation Type

Citation Type

Adjoint -classes on threefolds
We answer a question of Filip and Tosatti concerning a basepoint-free theorem for transcendental -classes on compact Kähler threefolds.
Correction to: A characterization of symplectic Grassmannians
We refer to our original paper, using the same notation.
EFFECTIVE BOUNDS FOR THE NUMBER OF MMP-SERIES OF A SMOOTH THREEFOLD
Abstract We prove that the number of MMP-series of a smooth projective threefold of positive Kodaira dimension and of Picard number equal to three is at most two.
The Minimal Model Program revisited
We give a light introduction to some recent developments in Mori theory, and to our recent direct proof of the finite generation of the canonical ring.
Hyperelliptic Gromov -Witten theory
HYPERELLIPTIC GROMOV-WITTEN THEORY
On the classification of non-big Ulrich vector bundles on surfaces and threefolds
In this paper, we classify Ulrich vector bundles that are not big on smooth complex surfaces and threefolds.
A generalization of Fulton’s conjecture for arbitrary groups
We prove a generalization of Fulton’s conjecture which relates intersection theory on an arbitrary flag variety to invariant theory.
The Nonvanishing problem for varieties with nef anticanonical bundle
. We prove that if ( X, ∆) is a threefold pair with mild singularities such that − ( K X + ∆) is nef, then the numerical class of − ( K X + ∆) is effective.
Rational curves on the moduli spaces of stable bundles
In this paper, we give an account of rational curves in moduli spaces of stable vector bundles on a smooth curve.
Math 260X: Rationality Questions in Algebraic Geometry
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References

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This paper studies the diophantine geometry of curves of genus greater than unity defined over a one-dimensional function field.
Algebraic Geometry
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On the Cone of divisors of Calabi-Yau fiber spaces
We prove some version of Morrison's conjecture on the cone of divisors for Calabi-Yau fiber spaces with non-trivial base pace whose total space is 3-dimensional.
FAMILIES OF ALGEBRAIC CURVES WITH FIXED DEGENERACIES
In this paper we prove that there exist only finitely many nonisomorphic and nonconstant curves of fixed genus, defined over a fixed function field and having bad reductions at a given finite set of…
Equivalences of derived categories and K3 surfaces
We consider derived categories of coherent sheaves on smooth projective variaties. We prove that any equivalence between them can be represented by an object on the product. Using this, we give a…
Stability conditions and crepant small resolutions
In this paper, we describe the spaces of stability conditions on the triangulated categories associated to three dimensional crepant small resolutions. The resulting spaces have chamber structures…
Equivalences of twisted K3 surfaces
We prove that two derived equivalent twisted K3 surfaces have isomorphic periods. The converse is shown for K3 surfaces with large Picard number. It is also shown that all possible twisted derived…
Stability conditions and Calabi–Yau fibrations
In this paper, we describe the spaces of stability conditions for the triangulated categories associated to three dimensional Calabi-Yau fibrations. We deal with two cases, the flat elliptic…
Stability Conditions on a Non-Compact Calabi-Yau Threefold
We study the space of stability conditions Stab(X) on the non-compact Calabi-Yau threefold X which is the total space of the canonical bundle of $$\mathbb{P}^2$$. We give a combinatorial description…
Families of canonically polarized varieties over surfaces
Shafarevich’s hyperbolicity conjecture asserts that a family of curves over a quasi-projective 1-dimensional base is isotrivial unless the logarithmic Kodaira dimension of the base is positive. More…
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