Birational automorphisms of higher-dimensional algebraic varieties.
Birational Finite Extensions of Mappings from a Smooth Variety
We present an example of finite mappings of algebraic varieties f:V → W, where V ⊂ kⁿ, , and such that and gdeg F = 1 < gdeg f (gdeg h means the number of points in the generic fiber of h). Thus, in some sense, the result of this note improves our result in J. Pure Appl. Algebra 148 (2000) where it was shown that this phenomenon can occur when V ⊂ kⁿ, with m ≥ n+2. In the case V,W ⊂ kⁿ a similar example does not exist.
Birational geometry of quadrics
We construct new birational maps between quadrics over a field. The maps apply to several types of quadratic forms, including Pfister neighbors, neighbors of multiples of a Pfister form, and half-neighbors. One application is to determine which quadrics over a field are ruled (that is, birational to the projective line times some variety) in a larger range of dimensions. We describe ruledness completely for quadratic forms of odd dimension at most 17, even dimension at most 10, or dimension 14....
Birational invariants of algebraic varieties.
Birational isomorphisms of four-dimensional quintics.
Birational models for varieties of Poncelet curves.
Birational moduli and nonabelian cohomology
Birational moduli and nonabelian cohomology, II
Birational Morphisms Factorizable by two Monoidal Transformations.
Birational morphisms of regular schemes
Birational Morphisms to lP2: An Ideal-Theoretic Perspective.
Birational Properties of Moduli spaces of stable locally free rank-2 sheaves on algebraic surfaces.