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The Mukai Conjecture for Fano Quiver Moduli
We verify the Mukai conjecture for Fano quiver moduli spaces associated to dimension vectors in the interior of the fundamental domain.
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Rationality of Fano Threefolds of Degree 18 over Non-closed Fields
We study unirationality and rationality of Fano threefolds of degree 18 over nonclosed fields.
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On the Quantum Cohomology of Blow-ups of Four-dimensional Quadrics
We propose a conjecture relevant to Galkin’s lower bound conjecture, and verify it for the blow-ups of a four-dimensional quadric at a point or along...
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Submanifolds of ℙn(l) with Splitting Tangent Sequence
Let l be a line in a projective space ℙ n . We consider the blowing up ℙ n ( l ) of ℙ n along l . Assume that X is a smooth closed subvariety of ℙ n . If the...
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Pseudoeffective thresholds and cohomology of twisted symmetric tensor fields on irreducible Hermitian symmetric spaces
Let X be an irreducible Hermitian symmetric space of compact type (IHSS for short). In this paper, we give the irreducible decomposition of Sym r T X ....
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Marked and Labelled Gushel–Mukai Fourfolds
We prove that the moduli stacks of marked and labelled Hodgespecial Gushel–Mukai fourfolds are isomorphic. As an application, we construct rational...
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The Generalized Roof F(1, 2,n): Hodge Structures and Derived Categories
We consider generalized homogeneous roofs, i.e. quotients of simply connected, semisimple Lie groups by a parabolic subgroup, which admit two...
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Rationality of Mukai Varieties over Non-closed Fields
We discuss birational properties of Mukai varieties, i.e., of higherdimensional analogues of prime Fano threefolds of genusg ∈ {7, 8, 9, 10} over an...
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Topics on the Geometry of Rational Homogeneous Spaces
This is a survey paper about a selection of results in complex algebraic geometry that appeared in the recent and less recent litterature, and in...
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Rigidity of certain admissible pairs of rational homogeneous spaces of Picard number 1 which are not of the subdiagram type
Recently, Mok and Zhang (2019) introduced the notion of admissible pairs ( X 0 , X ) of rational homogeneous spaces of Picard number 1 and proved...
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Basis log canonical thresholds, local intersection estimates, and asymptotically log del Pezzo surfaces
The purpose of this article is to develop techniques for estimating basis log canonical thresholds on logarithmic surfaces. To that end, we develop...
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On a Conjecture of Hong and Won
We give an explicit counter-example to a conjecture of Kyusik Hong and JoonyeongWon about α-invariants of polarized smooth del Pezzo surfaces of...
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Geometric Structures and Substructures on Uniruled Projective Manifolds
In a series of works on uniruled projective manifolds starting in the late 1990’s, Jun-Muk Hwang and the author have developed the basics of a...
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Cartan-Fubini type extension of holomorphic maps respecting varieties of minimal rational tangents
A fundamental result in the theory of minimal rational curves on projective manifolds is Cartan-Fubini extension theorem proved by Hwang and Mok,...
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On the Locus of Nonrigid Hypersurfaces
We show that the Zariski closure of the set of hypersurfaces of degree M in...
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Log canonical thresholds of del Pezzo surfaces in characteristic p
The global log canonical threshold of each non-singular complex del Pezzo surface was computed by Cheltsov. The proof used Kollár–Shokurov’s...
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The Mukai conjecture for log Fano manifolds
For a log Fano manifold ( X,D ) with D ≠ 0 and of the log Fano pseudoindex ≥2, we prove that the restriction homomorphism Pic( X ) → Pic( D ...
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Quartic del Pezzo surfaces over function fields of curves
We classify quartic del Pezzo surface fibrations over the projective line via numerical invariants, giving explicit examples for small values of the...