Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userThe Hodge-D-Conjecture fora Product of Elliptic Curves
171
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Let $X/C$ be a general product of elliptic curves. Our goal is to establish the Hodge-D-conjecture for $X$. We accomplish this when $dim X leq 5$. For $dim X geq 6$, we reduce the conjecture to a matrix rank condition that is amenable to computer calculation.
rate research
Read More
The Hodge conjecture is a major open problem in complex algebraic geometry. In this survey, we discuss the main cases where the conjecture is known, and also explain an approach by Griffiths-Green to solve the problem.
We review a combinatoric approach to the Hodge Conjecture for Fermat Varieties and announce new cases where the conjecture is true.
We show that very general hypersurfaces in odd-dimensional simplicial projective toric varieties verifying a certain combinatorial property satisfy the Hodge conjecture (these include projective spaces). This gives a connection between the Oda conjecture and Hodge conjecture. We also give an explicit criterion which depends on the degree for very general hypersurfaces for the combinatorial condition to be verified.
We prove that the product of an Enriques surface and a very general curve of genus at least 1 does not satisfy the integral Hodge conjecture for 1-cycles. This provides the first examples of smooth projective complex threefolds of Kodaira dimension zero for which the integral Hodge conjecture fails, and the first examples of non-algebraic torsion cohomology classes of degree 4 on smooth projective complex threefolds.
In this note, we prove effective semi-ampleness conjecture due to Prokhorov and Shokurov for a special case, more concretely, for Q-Gorenstein klt-trivial fibrations over smooth projective curves whose fibers are all klt log Calabi-Yau pairs of Fano type.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
