Related papers: On Quasismooth Weighted Complete Intersections
We prove that if a smooth variety with non-positive canonical class can be embedded into a weighted projective space of dimension $n$ as a well formed complete intersection and it is not an intersection with a linear cone therein, then the…
We classify Q-factorial Gorenstein Fano non-degenerate complete intersection threefolds in fake weighted projective spaces.
We classify smooth Fano weighted complete intersections of large codimension.
We show that smooth well formed weighted complete intersections have finite automorphism groups, with several obvious exceptions.
We survey what is known about Fano threefold weighted complete intersections from the point of view of birational rigidity.
We present a classification algorithm for Calabi-Yau complete intersections arising from nef-partitions in fake weighted projective spaces, allowing us to determine all such complete intersections up to dimension five. Furthermore, we…
We prove that there exist only finitely many families of Calabi-Yau quasismooth weighted complete intersections with every fixed dimension $m$. This generalizes a result of Johnson and Koll\'{a}r to higher codimensions.
We study the arithmetic of complete intersections in projective space over number fields. Our main results include arithmetic Torelli theorems and versions of the Shafarevich conjecture, as proved for curves and abelian varieties by…
We classify four-dimensional quasismooth weighted hypersurfaces with small canonical class, and verify a conjecture of Johnson and Kollar on infinite series of quasismooth hypersurfaces with anticanonical hyperplane section in the case of…
In this paper we compute genus 0 orbifold Gromov--Witten invariants of Calabi--Yau threefold complete intersections in weighted projective stacks, regardless of convexity conditions. The traditional quantumn Lefschetz principle may fail…
In this paper we describe all possible reduced complete intersection sets of points on Veronese surfaces. We formulate a conjecture for the general case of complete intersection subvarieties of any dimension and we prove it in the case of…
We obtain criteria for detecting complete intersections in projective varieties. Motivated by a conjecture of Hartshorne concerning subvarieties of projective spaces, we investigate situations when two-codimensional smooth subvarieties of…
We show Kawamata's effective nonvanishing conjecture (also known as the Ambro--Kawamata nonvanishing conjecture) holds for quasismooth weighted complete intersections of codimension $2$. Namely, for a quasismooth weighted complete…
We show that any quasismooth Fano threefold weighted complete intersections of type $(12, 14)$ in $\mathbb{P} (1, 2, 3, 4, 7, 11)$ is birationally solid.
The anticanonical complex generalizes the Fano polytope from toric geometry and has been used to study Fano varieties with torus action so far. We work out the case of complete intersections in toric varieties defined by non-degenerate…
In this paper we give a new and simplified proof of the variational Hodge conjecture for complete intersection cycles on a hypersurface in projective space.
Using a quadratic version of the Bott residue theorem, we give a quadratic refinement of the count of twisted cubic curves on hypersurfaces and complete intersections in a projective space.
We generalize the classical approach of describing the infinitesimal Torelli map in terms of multiplication in a Jacobi ring to the case of quasi-smooth complete intersections in weighted projective space. As an application, we prove the…
We generalize Givental's Theorem for complete intersections in smooth toric varieties in the Fano case. In particular, we find Gromov--Witten invariants of Fano varieties of dimension $\geq 3$, which are complete intersections in weighted…
In this paper, we define and study Clifford quadratic complete intersections. After showing some properties of Clifford quantum polynomial algebras, we show that there is a natural one-to-one correspondence between Clifford quadratic…