Biextensions alternées
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 positivity in dimension
In this paper we prove that for a nonsingular projective variety of dimension at most 4 and with non-negative Kodaira dimension, the Kodaira dimension of coherent subsheaves of is bounded from above by the Kodaira dimension of the variety. This implies the finiteness of the fundamental group for such an provided that has vanishing Kodaira dimension and non-trivial holomorphic Euler characteristic.
Birational Properties of Moduli spaces of stable locally free rank-2 sheaves on algebraic surfaces.
Bounding automorphism groups.
Bounds on the number of non-rational subfields of a function field.
Bridgeland-stable moduli spaces for -trivial surfaces
We give a one-parameter family of Bridgeland stability conditions on the derived category of a smooth projective complex surface and describe “wall-crossing behavior” for objects with the same invariants as when generates Pic and . If, in addition, is a or Abelian surface, we use this description to construct a sequence of fine moduli spaces of Bridgeland-stable objects via Mukai flops and generalized elementary modifications of the universal coherent sheaf. We also discover a natural...