Related papers: Complexity of del Pezzo surfaces with du Val singu…

We obtain an explicit formula for the number of rational cuspidal curves of a given degree on a del-Pezzo surface that pass through an appropriate number of generic points of the surface. This enumerative problem is expressed as an Euler…

Following Valloni, we study complex projective K3 surfaces having complex multiplication by rings of integers.

We completely classify K-stability of log del Pezzo hypersurfaces with index 2.

We complete the classification of regular generically free actions of finite groups on del Pezzo surfaces, up to birational equivalence. As a byproduct, we settle several open problems in equivariant birational geometry, e.g., we classify…

We study complex projective surfaces admitting a Poisson structure. We prove a classification theorem and count how many independent Poisson structures there are on a given Poisson surface.

We prove Manin's conjecture for a split singular quartic del Pezzo surface with singularity type $2\Aone$ and eight lines. This is achieved by equipping the surface with a conic bundle structure. To handle the sum over the family of conics,…

We compute symplectic cohomology for Milnor fibres of certain compound Du Val singularities that admit small resolution by using homological mirror symmetry. Our computations suggest a new conjecture that the existence of a small resolution…

After a short summary of known results on surface-complexity of closed 3-manifolds, we will classify all closed orientable 3-manifolds with surface-complexity one.

We prove that for Du Val del Pezzo surfaces of degree one with Picard rank two, the existence of an anticanonical polar cylinder implies the ample polar cylindricity.

For split smooth Del Pezzo surfaces, we analyse the structure of the effective cone and prove a recursive formula for the value of alpha, appearing in the leading constant as predicted by Peyre of Manin's conjecture on the number of…

We investigate geometric properties of surfaces given by certain formulae. In particular, we calculate the singular curvature and the limiting normal curvature of such surfaces along the set of singular points consisting of singular points…

We describe a method to evaluate multivariate polynomials over a finite field and discuss its multiplicative complexity.

For a regular del Pezzo surface $X$, we prove that $|-12K_X|$ is very ample. Furthermore, we also give an explicit upper bound for the volume $K_X^2$ which depends only on $[k : k^p]$ for the base field $k$. As a consequence, we obtain the…

Real, complex, and tropical algebraic geometry join forces in a new branch of mathematical physics called positive geometry. We develop the positive geometry of del Pezzo surfaces and their moduli spaces, viewed as very affine varieties.…

We construct a klt del Pezzo surface which is not globally F-split, over any algebraically closed field of positive characteristic.

We study the birational rigidity problem for smooth Mori fibrations on del Pezzo surfaces of degree 1 and 2. For degree 1 we obtain a complete description of rigid and non-rigid cases.

We classify isoparametric hypersurfaces in complex hyperbolic spaces.

We obtain a formula for the number of genus one curves with a fixed complex structure of a given degree on a del-Pezzo surface that pass through an appropriate number of generic points of the surface. This enumerative problem is expressed…

We introduce higher simplicial complexity of a simplicial complex $K$ and higher combinatorial complexity of a finite space $P$ (i.e. $P$ is a finite poset). We relate higher simplicial complexity with higher topological complexity of $|K|$…

This is an expanded version of the two papers "Interpolation of Varieties of Minimal Degree" and "Interpolation Problems: Del Pezzo Surfaces." It is well known that one can find a rational normal curve in $\mathbb P^n$ through $n+3$ general…