Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userMaximal Chow constant and cohomologically constant fibrations
260
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Motivated by the study of rationally connected fibrations (and the MRC quotient) we study different notions of birationally simple fibrations. We say a fibration of smooth projective varieties is Chow constant if pushforward induces an isomorphism on the Chow group of 0-cycles. Likewise we say a fibration is cohomologically constant if pullback induces an isomorphism on holomorphic p-forms for all p. Our main result is the construction of maximal Chow constant and cohomologically constant fibrations. The paper is largely self contained and we prove a number of basic properties of these fibrations. One application is to the classification of rationalizations of singularities of cones. We also consider consequences for the Chow groups of the generic fiber of a Chow constant fibration.
rate research
Read More
For an arbitrary del Pezzo surface S, we compute alpha(S), which is the volume of a certain polytope in the dual of the effective cone of S, using Magma and Polymake. The constant alpha(S) appears in Peyres conjecture for the leading term in the asymptotic formula for the number of rational points of bounded height on S over number fields.
We introduce a theory of multigraded Cayley-Chow forms associated to subvarieties of products of projective spaces. Two new phenomena arise: first, the construction turns out to require certain inequalities on the dimensions of projections; and second, in positive characteristic the multigraded Cayley-Chow forms can have higher multiplicities. The theory also provides a natural framework for understanding multifocal tensors in computer vision.
We prove that the Chow motives of two smooth cubic fourfolds whose Kuznetsov components are Fourier-Mukai derived-equivalent are isomorphic as Frobenius algebra objects. As a corollary, we obtain that there exists a Galois-equivariant isomorphism between their l-adic cohomology Frobenius algebras. We also discuss the case where the Kuznetsov component of a smooth cubic fourfold is Fourier-Mukai derived-equivalent to a K3 surface.
We prove that the perverse Leray filtration for the Hitchin morphism is locally constant in families, thus providing some evidence towards the validity of the $P=W$ conjecture due to de Cataldo, Hausel and Migliorini in non Abelian Hodge theory.
We show that the M-canonical map of an n-dimensional complex projective manifold X of Kodaira dimension two is birational to an Iitaka fibration for a computable positive integer M. M depends on the index b of a general fibre F of the Iitaka fibration and on the Betti number of the canonical covering of F, In particular, M is a universal constant if the dimension n is smaller than or equal to 4.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
