4 citations · 8 across the 8 of their papers we have counts for
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K3 structures from singular Fano varieties
Enrico Fatighenti
We survey some results obtained in our quest for Fano varieties of K3 type and discuss why exploring the singular world might be interesting for discovering new K3 structures.
On the geometry of some quiver zero loci Fano fourfolds (with an appendix by E. Kalashnikov and F. Tufo)
Enrico Fatighenti, Fabio Tanturri, Federico Tufo
In this paper, we study 170 families of quiver flag zero loci Fano fourfolds as described by Kalashnikov. We interpret those manifolds as zero loci of sections of homogeneous vecto…
Even nodal surfaces of K3 type
Marcello Bernardara, Enrico Fatighenti, Grzegorz Kapustka +4
We study Fano fourfolds of K3 type with a conic bundle structure. We construct direct geometrical links between these fourfolds and hyperKähler varieties. As a result we describe f…
Topics on Fano varieties of K3 type
Enrico Fatighenti
This is a survey paper about a selection of recent results on the geometry of a special class of Fano varieties, which are called of K3 type. The focus is mostly Hodge-theoretical,…
Hilbert squares of degeneracy loci
Enrico Fatighenti, Francesco Meazzini, Giovanni Mongardi +1
Let be the first degeneracy locus of a morphism of vector bundles corresponding to a general matrix of linear forms in . We prove that, under certain positivity c…
Fano fourfolds of K3 type
Marcello Bernardara, Enrico Fatighenti, Laurent Manivel +1
We produce a list of 64 families of Fano fourfolds of K3 type, extracted from our database of at least 634 Fano fourfolds constructed as zero loci of general global sections of com…
The generalized roof F(1,2,n): Hodge structures and derived categories
Enrico Fatighenti, Michał Kapustka, Giovanni Mongardi +1
We consider generalized homogeneous roofs, i.e. quotients of simply connected, semisimple Lie groups by a parabolic subgroup, which admit two projective bundle structures. Given a…
Polyvector fields for Fano 3-folds
Pieter Belmans, Enrico Fatighenti, Fabio Tanturri
We compute the Hochschild-Kostant-Rosenberg decomposition of the Hochschild cohomology of Fano 3-folds. This is the first step in understanding the non-trivial Gerstenhaber algebra…
Fano 3-folds from homogeneous vector bundles over Grassmannians
Lorenzo De Biase, Enrico Fatighenti, Fabio Tanturri
We rework the Mori-Mukai classification of Fano 3-folds, by describing each of the 105 families via biregular models as zero loci of general global sections of homogeneous vector b…
Nested varieties of K3 type
Marcello Bernardara, Enrico Fatighenti, Laurent Manivel
Using geometrical correspondences induced by projections and two-steps flag varieties, and a generalization of Orlov's projective bundle theorem, we relate the Hodge structures and…
Fano varieties of K3 type and IHS manifolds
Enrico Fatighenti, Giovanni Mongardi
We construct several new families of Fano varieties of K3 type. We give a geometrical explanation of the K3 structure and we link some of them to projective families of irreducible…
A note on a Griffiths-type ring for complete intersections in Grassmannians
Enrico Fatighenti, Giovanni Mongardi
We calculate a Griffiths-type ring for smooth complete intersection in Grassmannians. This is the analogue of the classical Jacobian ring for complete intersections in projective s…