Related papers: On Gorenstein Fano toric complete intersections
We give a bound on the minimal number of singularities of a nodal projective complete intersection threefold which contains a smooth complete intersection surface that is not a Cartier divisor.
In this thesis, I determine a bound on the defect of terminal Gorenstein quartic 3-folds. More generally, I study the defect of terminal Gorenstein Fano 3-folds of Picard rank 1 and genus at least 3. I state a geometric "motivation" of non…
We compute the integral homology (including torsion), the topological K-theory, and the Hodge structure on cohomology of Calabi-Yau threefold hypersurfaces and complete intersections in Gorenstein toric Fano varieties. The methods are…
We classify nonrational Fano threefolds $X$ with terminal Gorenstein singularities such that $\mathrm{\rk}\, \mathrm{\Pic}(X)=1$, $(-K_X)^3\ge 8$, and $\mathrm{\rk}\, \mathrm{\Cl}(X)\le 2$.
We classify the non-toric, $\mathbb{Q}$-factorial, Gorenstein, Fano threefolds of Picard number one with an effective $\mathbb{K}^*$-action and maximal orbit quotient $\mathbb{P}_2$.
We provide a complete classification of Fano threefolds X having canonical Gorenstein singularities and the anticanonical degree (-KX)^3 equal 64.
We survey what is known about Fano threefold weighted complete intersections from the point of view of birational rigidity.
In this paper, we classify projective toric birational morphisms from Gorenstein toric 3-folds onto the 3-dimensional affine space with relatively ample anti-canonical divisors.
We study Q-factorial terminal Fano 3-folds whose equations are modelled on those of the Segre embedding of P^2 x P^2. These lie in codimension 4 in their total anticanonical embedding and have Picard rank 2. They fit into the current state…
We show that a non-toric $\mathbb{Q}$-factorial terminal Fano threefold of Picard rank $1$ and Fano index $13$ is a weighted hypersurface of degree $12$ in $\mathbb{P}(3,4,5,6,7)$.
We classify all Gorenstein Fano threefolds with at worst canonical singularities for which the anticanonical system has a nonempty base locus.
We classify Q-Fano threefolds of Fano index > 2 and big degree.
We find at least 527 new four-dimensional Fano manifolds, each of which is a complete intersection in a smooth toric Fano manifold.
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.
For fixed degree $d\leq 12$, we study the Hilbert scheme of degree $d$ smooth Fano threefolds in their anticanonical embeddings. We use this to classify all possible degenerations of these varieties to toric Fano varieties with at most…
We classify three-dimensional Fano varieties with canonical Gorenstein singularities of degree bigger than 64.
We compute the quantum Euler class of Fano complete intersections X in a projective space. In particular, we prove a recent conjecture of A. Buch and R. Pandharipande. Finally we apply our result to obtain formulas for the virtual Tevelev…
We classify smooth Fano threefolds with infinite automorphism groups.
Complete intersections inside rational homogeneous varieties provide interesting examples of Fano manifolds. For example, if $X = \cap_{i=1}^r D_i \subset G/P$ is a general complete intersection of $r$ ample divisors such that $K_{G/P}^*…
We classify Fano threefolds with only Gorenstein terminal singularities and Picard number greater than 1 satisfying an additional assumption that the $G$-invariant part of the Weil divisor class group is of rank 1 with respect to an action…