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A boundedness theorem for morphisms between threefolds

Ekatarina Amerik, Marat Rovinsky, Antonius Van de Ven (1999)

Annales de l'institut Fourier

The main result of this paper is as follows: let $X, Y$ be smooth projective threefolds (over a field of characteristic zero) such that $b_{2} (X) = b_{2} (Y) = 1$ . If $Y$ is not a projective space, then the degree of a morphism $f : X \to Y$ is bounded in terms of discrete invariants of $X$ and $Y$ . Moreover, suppose that $X$ and $Y$ are smooth projective $n$ -dimensional with cyclic Néron-Severi groups. If $c_{1} (Y) = 0$ , then the degree of $f$ is bounded iff $Y$ is not a flat variety. In particular, to prove our main theorem we show the non-existence of a flat 3-dimensional...

A result on $m$ -flats in $A_{k}^{n}$

P. C. Craighero (1986)

Rendiconti del Seminario Matematico della Università di Padova

A simpler proof of toroidalization of morphisms from 3-folds to surfaces

Steven Dale Cutkosky (2013)

Annales de l’institut Fourier

We give a simpler and more conceptual proof of toroidalization of morphisms of 3-folds to surfaces, over an algebraically closed field of characteristic zero. A toroidalization is obtained by performing sequences of blow ups of nonsingular subvarieties above the domain and range, to make a morphism toroidal. The original proof of toroidalization of morphisms of 3-folds to surfaces is much more complicated.

We describe a bound on the degree of the generators for some adjoint rings on surfaces and threefolds.

Currently displaying 1 – 20 of 36

Page 1 Next

Displaying 1 – 20 of 36

A boundedness theorem for morphisms between threefolds

A result on $m$ -flats in $A_{k}^{n}$

A simpler proof of toroidalization of morphisms from 3-folds to surfaces

Abschätzungen für die Anzahl der holomorphen Abbildungen zwischen algebraischen Räumen.

Atkin-Lehner involutions and class number residuality

Biextensions alternées

Bounds on the number of non-rational subfields of a function field.

Classification of algebraic varieties, I

Effective finite generation for adjoint rings

Endomorphism algebras of complex tori.

Equations for Endomorphisms of Abelian Varieties.

Holomorphe Abbildungen zwischen quasiprojektiven Räumen.

Joins of schemes, linear projections

Lifting endomorphisms of formal $A$ -modules

Maps onto certain Fano threefolds.

Normal affine surfaces properly dominated by C x C.

On a conjecture of Xiao.

On special projections of varieties: Epitome to a theorem of Beniamino Segre.

On the blowing down problem in C-analytic geometry.

On the generic injectivity of the Gauss map in positive characteristic.

Currently displaying 1 – 20 of 36