17 citations · 107 across the 41 of their papers we have counts for
46 papers
Moduli spaces of varieties of general type are naturally of log general type
Sebastian Casalaina-Martin, Shend Zhjeqi
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 resul…
Moduli spaces of snc klt KSBA stable pairs are naturally of log general type
Sebastian Casalaina-Martin, Shend Zhjeqi
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…
Foliations, slope stability, and positivity of log canonical bundles on Deligne-Mumford stacks
Sebastian Casalaina-Martin, Shend Zhjeqi
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 prope…
Movable curve classes and slope stability on Deligne-Mumford stacks
Sebastian Casalaina-Martin, Shend Zhjeqi
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…
Positivity in the context of Hodge modules and Higgs bundles on Deligne-Mumford stacks
Sebastian Casalaina-Martin, Shend Zhjeqi
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…
Regular homomorphisms, with a twist
Jeff Achter, Sebastian Casalaina-Martin, Charles Vial
Let be a variety over a field, and an abelian variety. A regular homomorphism to (in codimension ) induces, for every smooth geometrically connected pointed -…
Three approaches to a categorical Torelli theorem for cubic threefolds of non-Eckardt type via the equivariant Kuznetsov components
Sebastian Casalaina-Martin, Xianyu Hu, Xun Lin +2
Let be a cubic threefold with a non-Eckardt type involution . Our first main result is that the -equivariant category of the Kuznetsov component $\mathcal{K}u_{\mathbb{Z}…
The birational geometry of moduli of cubic surfaces and cubic surfaces with a line
Sebastian Casalaina-Martin, Samuel Grushevsky, Klaus Hulek
We determine the cones of effective and nef divisors on the toroidal compactification of the ball quotient model of the moduli space of complex cubic surfaces with a chosen line. F…
Putting the p back in Prym
Jeff Achter, Sebastian Casalaina-Martin
After Jacobians of curves, Prym varieties are perhaps the next most studied abelian varieties. They turn out to be quite useful in a number of contexts. For technical reasons, ther…
Images of abelian schemes
Jeff Achter, Sebastian Casalaina-Martin, Jonathan Wise
We provide some conditions for the image of a morphism of abelian schemes to again be an abelian scheme. For context, in characteristic 0, the image is always an abelian scheme; in…
The moduli space of cubic threefolds with a non-Eckardt type involution via intermediate Jacobians
Sebastian Casalaina-Martin, Lisa Marquand, Zheng Zhang
There are two types of involutions on a cubic threefold: the Eckardt type (which has been studied by the first named and the third named authors) and the non-Eckardt type. Here we…
A complete answer to Albanese base change for incomplete varieties
Jeff Achter, Sebastian Casalaina-Martin, Charles Vial
Albanese varieties provide a standard tool in algebraic geometry for converting questions about varieties in general, to questions about Abelian varieties. A result of Serre provid…
Non-isomorphic smooth compactifications of the moduli space of cubic surfaces
Sebastian Casalaina-Martin, Samuel Grushevsky, Klaus Hulek +1
The moduli space of complex cubic surfaces has three different, but isomorphic, compact realizations: as a GIT quotient, as a Baily--Borel compactification of a ball quotient, and…
The Walker Abel-Jacobi map descends
Jeff Achter, Sebastian Casalaina-Martin, Charles Vial
For a complex projective manifold, Walker has defined a regular homomorphism lifting Griffiths' Abel-Jacobi map on algebraically trivial cycle classes to a complex abelian variety,…
Decomposition of the diagonal, intermediate Jacobians, and universal codimension-2 cycles in positive characteristic
Jeff Achter, Sebastian Casalaina-Martin, Charles Vial
We consider the connections among algebraic cycles, abelian varieties, and stable rationality of smooth projective varieties in positive characteristic. Recently Voisin constructed…
On the image of the second l-adic Bloch map
Jeff Achter, Sebastian Casalaina-Martin, Charles Vial
For a smooth projective geometrically uniruled threefold defined over a perfect field we show that there exists a canonical abelian variety over the field, namely the second algebr…
The moduli space of cubic surface pairs via the intermediate Jacobians of Eckardt cubic threefolds
Sebastian Casalaina-Martin, Zheng Zhang
We study the moduli space of pairs consisting of a smooth cubic surface and a smooth hyperplane section, via a Hodge theoretic period map due to Laza, Pearlstein, and the second na…
A functorial approach to regular homomorphisms
Jeff Achter, Sebastian Casalaina-Martin, Charles Vial
Classically, regular homomorphisms have been defined as a replacement for Abel--Jacobi maps for smooth varieties over an algebraically closed field. In this work, we interpret regu…
Cohomology of the moduli space of cubic threefolds and its smooth models
Sebastian Casalaina-Martin, Samuel Grushevsky, Klaus Hulek +1
We compute and compare the (intersection) cohomology of various natural geometric compactifications of the moduli space of cubic threefolds: the GIT compactification and its Kirwan…
Normal functions for algebraically trivial cycles are algebraic for arithmetic reasons
Jeff Achter, Sebastian Casalaina-Martin, Charles Vial
For families of smooth complex projective varieties we show that normal functions arising from algebraically trivial cycle classes are algebraic, and defined over the field of defi…
An introduction to moduli stacks, with a view towards Higgs bundles on algebraic curves
Sebastian Casalaina-Martin, Jonathan Wise
This article is based in part on lecture notes prepared for the summer school "The Geometry, Topology and Physics of Moduli Spaces of Higgs Bundles" at the Institute for Mathematic…
Multi-Observation Elicitation
Sebastian Casalaina-Martin, Rafael Frongillo, Tom Morgan +1
We study loss functions that measure the accuracy of a prediction based on multiple data points simultaneously. To our knowledge, such loss functions have not been studied before i…
Derived equivalent threefolds, algebraic representatives, and the coniveau filtration
Jeff Achter, Sebastian Casalaina-Martin, Charles Vial
A conjecture of Orlov predicts that derived equivalent smooth projective varieties over a field have isomorphic Chow motives. The conjecture is known for curves, and was recently o…
Distinguished models of intermediate Jacobians
Jeff Achter, Sebastian Casalaina-Martin, Charles Vial
We show that the image of the Abel-Jacobi map admits functorially a model over the field of definition, with the property that the Abel-Jacobi map is equivariant with respect to th…