6 citations · 15 across the 18 of their papers we have counts for
21 papers
Enriques surfaces with non-generic non-degeneracy
Riccardo Moschetti, Franco Rota, Luca Schaffler
We study the non-degeneracy invariant of complex Enriques surfaces in families. Our first main result shows that cannot increase under specializat…
Fineness and smoothness of a KSBA moduli of marked cubic surfaces
Hanlong Fang, Luca Schaffler, Xian Wu
By work of Gallardo-Kerr-Schaffler, it is known that Naruki's compactification of the moduli space of marked cubic surfaces is isomorphic to the normalization of the Kollár, Shephe…
An explicit wall crossing for the moduli space of hyperplane arrangements
Patricio Gallardo, Luca Schaffler
The moduli space of hyperplanes in projective space has a family of geometric and modular compactifications that parametrize stable hyperplane arrangements with respect to a weight…
Simplices osculating rational normal curves
Alessio Caminata, Enrico Carlini, Luca Schaffler
A classical result of von Staudt states that if eight planes osculate a twisted cubic curve and we divide them into two groups of four, then the eight vertices of the corresponding…
Compact moduli of Enriques surfaces with a numerical polarization of degree 2
Valery Alexeev, Philip Engel, D. Zack Garza +1
We describe a geometric, stable pair compactification of the moduli space of Enriques surfaces with a numerical polarization of degree 2, and identify it with a semitoroidal compac…
The non-degeneracy invariant of Brandhorst and Shimada's families of Enriques surfaces
Riccardo Moschetti, Franco Rota, Luca Schaffler
Brandhorst and Shimada described a large class of Enriques surfaces, called -generic, for which they gave generators for the automorphism groups and calculated the…
Determinantal varieties from point configurations on hypersurfaces
Alessio Caminata, Han-Bom Moon, Luca Schaffler
We consider the scheme parametrizing ordered points in projective space that lie on a common hypersurface of degree . We show that this scheme has…
Unimodal singularities and boundary divisors in the KSBA moduli of a class of Horikawa surfaces
Patricio Gallardo, Gregory Pearlstein, Luca Schaffler +1
Smooth minimal surfaces of general type with , , and constitute a fundamental example in the geography of algebraic surfaces, and the 28-dimensional moduli spac…
Gaussian likelihood geometry of projective varieties
Sandra Di Rocco, Lukas Gustafsson, Luca Schaffler
We explore the maximum likelihood degree of a homogeneous polynomial on a projective variety , , which generalizes the concept of Gaussian maximum likelih…
A computational view on the non-degeneracy invariant for Enriques surfaces
Riccardo Moschetti, Franco Rota, Luca Schaffler
For an Enriques surface , the non-degeneracy invariant retains information on the elliptic fibrations of and its polarizations. In the current paper, we int…
Families of pointed toric varieties and degenerations
Sandra Di Rocco, Luca Schaffler
The Losev-Manin moduli space parametrizes pointed chains of projective lines. In this paper we study a possible generalization to families of pointed degenerate toric varieties. Ge…
Compactifications of moduli of points and lines in the projective plane
Luca Schaffler, Jenia Tevelev
Projective duality identifies the moduli spaces and parametrizing linearly general configurations of points in and lines in…
Geometric interpretation of toroidal compactifications of moduli of points in the line and cubic surfaces
Patricio Gallardo, Matt Kerr, Luca Schaffler
It is known that some GIT compactifications associated to moduli spaces of either points in the projective line or cubic surfaces are isomorphic to Baily-Borel compactifications of…
Point configurations, phylogenetic trees, and dissimilarity vectors
Alessio Caminata, Noah Giansiracusa, Han-Bom Moon +1
In 2004 Pachter and Speyer introduced the higher dissimilarity maps for phylogenetic trees and asked two important questions about their relation to the tropical Grassmannian. Mult…
Decomposition of Lagrangian classes on K3 surfaces
Kuan-Wen Lai, Yu-Shen Lin, Luca Schaffler
We study the decomposability of a Lagrangian homology class on a K3 surface into a sum of classes represented by special Lagrangian submanifolds, and develop criteria for it in ter…
A Pascal's Theorem for rational normal curves
Alessio Caminata, Luca Schaffler
Pascal's Theorem gives a synthetic geometric condition for six points in to lie on a conic. Namely, that the intersection points $\overline{ab}\cap\over…
KSBA compactification of the moduli space of K3 surfaces with purely non-symplectic automorphism of order four
Han-Bom Moon, Luca Schaffler
We describe a compactification by KSBA stable pairs of the five-dimensional moduli space of K3 surfaces with purely non-symplectic automorphism of order four and $U(2)\oplus D_4^{\…
Equations for point configurations to lie on a rational normal curve
Alessio Caminata, Noah Giansiracusa, Han-Bom Moon +1
The parameter space of ordered points in projective -space that lie on a rational normal curve admits a natural compactification by taking the Zariski closure in $(\mathbb{P…
K3 surfaces with symplectic action
Luca Schaffler
Let be a finite abelian group which acts symplectically on a K3 surface. The Néron-Severi lattice of the projective K3 surfaces admitting symplectic action and with minimal…
The KSBA compactification of the moduli space of -polarized Enriques surfaces
Luca Schaffler
We describe a compactification by stable pairs (also known as KSBA compactification) of the -dimensional family of Enriques surfaces which arise as the -covers o…
On the cone of effective 2-cycles on
Luca Schaffler
Fulton's question about effective -cycles on for can be answered negatively by appropriately lifting to the Keel-Vermeire div…