Related papers: Singular elliptic genus of normal surfaces

Let $(X,L)$ be a polarized K3 surface of genus $g$ and $C_{en} \subset X$ be the curve of singular points of nodal elliptic curves in $|L|$. When $(X,L)$ is generic of genus two, Huybrechts observed that the curve $C_{en}$ is a constant…

We prove that the outer Lipschitz geometry of a germ $(X,0)$ of a normal complex surface singularity determines a large amount of its analytic structure. In particular, it follows that any analytic family of normal surface singularities…

We prove that the genus of the Turaev surface of a link diagram is determined by a graph whose vertices correspond to the boundary components of the maximal alternating regions of the link diagram. Furthermore, we use these graphs to…

We investigate fibrations by non-hyperelliptic curves of arithmetic genus three and geometric genus one in characteristic two. Assuming that there is only one moving singularity and that its image in the Frobenius pullback of the fibration…

We prove that every nontrivial principal $G_m$-bundle over a complete uniformly rational variety is algebraically elliptic in the sense of Gromov.

We study monodromy groups of elliptic fibrations over the projective line.

We study genus 2 covers of relative elliptic curves over an arbitrary base in which 2 is invertible. Particular emphasis lies on the case that the covering degree is 2. We show that the data in the "basic construction" of genus 2 covers of…

We revisit the construction of elliptic class given by Borisov and Libgober for singular algebraic varieties. Assuming torus action we adjust the theory to equivariant local situation. We study theta function identities having geometric…

We show that a very general Jacobian elliptic surface is determined by its polarized rational Hodge structure, subject to various constraints on the irregularity and the geometric genus.

We show that elliptic classes introduced in our earlier paper for spaces with infinite fundamental groups yield Novikov's type higher elliptic genera which are invariants of K-equivalence. This include, as a special case, the birational…

We prove that the Brauer group of the generic diagonal surface of arbitrary degree is trivial. The same method is applied to surfaces whose equation can be written as the sum of two bilinear forms. This uses a general criterion for the…

In this article, we construct the first example of an elliptic surface with infinitely many smooth \((-1)\)-curves of genus \(g>1\), settling an open question of Bauer et al. [Duke Math. J. \textbf{162} (10) (2013), 1877-1894].

We prove the Lipman-Zariski conjecture for complex surface singularities with $p_g - g - b \le 2$. Here $p_g$ is the geometric genus, $g$ is the sum of the genera of the exceptional curves and $b$ is the first Betti number of the dual…

Using the path lattice cohomology we provide a conceptual topological characterization of the geometric genus for certain complex normal surface singularities with rational homology sphere links, which is uniformly valid for all…

We provide combinatorial/topological formula for the multiplicity of a complex analytic normal surface singularity whenever the analytic structure on the fixed topological type is generic.

We study relatively minimal surfaces equipped with a strongly isotrivial elliptic fibration in positive characteristic by means of the notion of equivariantly normal curves introduced and developed recently by Brion. Such surfaces are…

A log symplectic manifold is a complex manifold equipped with a complex symplectic form that has simple poles on a hypersurface. The possible singularities of such a hypersurface are heavily constrained. We introduce the notion of an…

We construct genus one curves on base extensions of generic Severi--Brauer varieties of a given index and period which are versal objects for families of geometrically elliptic normal curves. We also compute the periods and indices of these…

We undertake a systematic study of Lipschitz Normally Embedded normal complex surface germs. We prove in particular that the topological type of such a germ determines the combinatorics of its minimal resolution which factors through the…

We define a new elliptic genus psi on the complex bordism ring. With coefficients in Z[1/2], we prove that it induces an isomorphism of the complex bordism ring modulo the ideal which is generated by all differences P(E)-P(E*) of projective…