arXiv subjects

Shend Zhjeqi

Publications and source records attributed to Shend Zhjeqi.

5 recordsLinked to original sources

arXiv2026

Moduli spaces of varieties of general type are naturally of log general type

We generalize work of Popa-Schnell on Viehweg hyperbolicity for smooth projective varieties to the case of smooth Deligne-Mumford stacks. The results of Popa-Schnell build on results of Viehweg-Zuo, utilize a result of Campana-Păun, and extend results of Kebekus-Kovács and Patakfalvi. We show that if a smooth proper DM stack with projective coarse moduli space parameterizes a family of varieties of general type having maximal variation, then the natural log canonical bundle of the stack is big. We also consider implications for the coarse moduli space of the stack, and apply the results to several standard moduli spaces.

math.AG↗

arXiv2026

Moduli spaces of snc klt KSBA stable pairs are naturally of log general type

We generalize work of Wei-Wu on Viehweg hyperbolicity for families of stable pairs over smooth projective varieties to the case of smooth Deligne-Mumford stacks. The results of Wei-Wu build on results of Popa-Schnell and Viehweg-Zuo, utilize a result of Campana-Păun, and extend results of Kebekus-Kovács and Patakfalvi. We apply our results to smooth proper moduli stacks parameterizing generically klt relatively simple normal crossings KSBA stable pairs, showing that such moduli stacks naturally have big log canonical bundles. We also consider implications for their coarse moduli spaces.

math.AG↗

arXiv2026

Foliations, slope stability, and positivity of log canonical bundles on Deligne-Mumford stacks

We generalize some results of Campana-Păun regarding foliations, slope stability, and positivity of log canonical bundles on smooth projective varieties to the case of smooth proper DM stacks admitting projective coarse moduli spaces. This paper is the third in a series aiming to generalize results of Popa-Schnell and Wei-Wu on Viehweg hyperbolicity to the setting of DM stacks, and in particular, to certain KSBA moduli spaces.

math.AG↗

arXiv2026

Movable curve classes and slope stability on Deligne-Mumford stacks

We generalize some results in the literature on movable curve classes and slope stability of coherent sheaves on smooth projective varieties to the case of smooth proper DM stacks admitting projective coarse moduli spaces. As an application, we establish a Bogomolov-Gieseker inequality on such stacks. This paper is the second in a series aiming to generalize results of Popa-Schnell and Wei-Wu on Viehweg hyperbolicity to the setting of DM stacks, and in particular, to certain KSBA moduli spaces.

math.AG↗

arXiv2026

Positivity in the context of Hodge modules and Higgs bundles on Deligne-Mumford stacks

We generalize positivity results due to Popa-Wu and Popa-Schnell for Hodge modules and Higgs bundles on smooth projective varieties to the case of smooth proper DM stacks admitting projective coarse moduli spaces. This paper is the first in a series aiming to generalize results of Popa-Schnell and Wei-Wu on Viehweg hyperbolicity to the setting of DM stacks, and in particular, to certain KSBA moduli spaces.

math.AG↗