12 papers
An algebraic comparison of -stability and -stability
Theodoros Stylianos Papazachariou
We establish a uniform quantitative comparison between the non-Archimedean Mabuchi functional and the Darvas--Zhang quantised Mabuchi functional. For a smooth polarised variety wit…
-reductivity and -completeness for adjoint Fano foliated structures
Theodoros Stylianos Papazachariou
We prove the valuative criteria of -reductivity and -completeness for the moduli problem of -K-semistable adjoint Fano foliated structures. We develop a mixed Ding theory…
Singularity criteria for K-stability of adjoint foliated structures
Theodoros Stylianos Papazachariou
We prove singularity criteria for the -K-stability of adjoint foliated structures. We first show that K-semistability of adjoint foliated structures implies log canonicity by ex…
K-stability of adjoint foliated structures
Theodoros Stylianos Papazachariou
We introduce a notion of K-stability for adjoint foliated structures via test configurations and the foliated Donaldson-Futaki invariant. We prove reduction to special test configu…
Nets of quadric surfaces and plane cubics and their GIT stability
Masafumi Hattori, Theodoros Stylianos Papazachariou, Aline Zanardini
A general net of quadric surfaces, together with a choice of a base point, defines a net of plane cubics via the Gale transformation of the remaining seven base points. To both net…
K-Moduli of Fano Threefolds of Family 3.3
Erroxe Etxabarri-Alberdi, James Matthew Jones, Theodoros Stylianos Papazachariou
We explicitly fully describe the K-moduli space of Fano threefold family number 3.3. We first show that K-semistable Fano varieties with volume greater than 18 are Gorenstein canon…
K-moduli of log del Pezzo pairs and variations of GIT
Jesus Martinez-Garcia, Theodoros Stylianos Papazachariou, Junyan Zhao
We study the K-moduli of log del Pezzo pairs formed by a del Pezzo surface of degree and an anti-canonical divisor. These moduli spaces naturally depend on one parameter, provi…
GIT stability of divisors in products of projective spaces
Ioannis Karagiorgis, Theresa A. Ortscheidt, Theodoros S. Papazachariou
We study GIT stability of divisors in products of projective spaces. We first construct a finite set of one-parameter subgroups sufficient to determine the stability of the GIT quo…
One-dimensional components in the K-moduli of smooth Fano 3-folds
Hamid Abban, Ivan Cheltsov, Elena Denisova +5
By identifying K-polystable limits in 4 specific deformations families of smooth Fano 3-folds, we complete the classification of one-dimensional components in the K-moduli space of…
On divisorial stability of finite covers
Ruadhaí Dervan, Theodoros Stylianos Papazachariou
Divisorial stability of a polarised variety is a stronger - but conjecturally equivalent - variant of uniform K-stability introduced by Boucksom-Jonsson. Whereas uniform K-stabilit…
GIT of complete intersections and log canonical thresholds
Theodoros Stylianos Papazachariou
We establish a link between the GIT stability of complete intersections of same degree hypersurfaces in the same ambient projective space, which can be parametrised as tuples in a…
K-moduli of log Fano complete intersections
Theodoros Stylianos Papazachariou
We explicitly describe the K-moduli compactifications and wall crossings of log pairs formed by a Fano complete intersection of two quadric threefolds and a hyperplane, by construc…