Related papers: Weighted complete intersection del Pezzo surfaces

In this paper we consider Gorenstein stable surfaces with $K^2_X=1$ and positive geometric genus. Extending classical results, we show that such surfaces admit a simple description as weighted complete intersection. We exhibit a wealth of…

We construct two types of wellformed and quasismooth biregular models (infinite series) of rigid orbifold del Pezzo surfaces having their (sub) anti-canonical embeddings in $\mathbb P^6(w_i) $. One type of model contains a family of rigid…

We get sharp degree bound for generic smoothness and connectedness of the space of conics in low degree complete intersections which generalizes the old work about Fano scheme of lines on Hypersurfaces.

In this paper we classify all potentially G-birationally rigid del Pezzo threefolds of degree 4 and their automorphism groups and prove the G-birational rigidity of one of them

Some classification results for ample vector bundles of rank 2 on Hirzebruch surfaces, and on Del Pezzo surfaces, are obtained. In particular, we classify rank-2 ample vector bundles with $c_2$ less than 7 on Hirzebruch surfaces, and with…

We compute the Chow quotient of the complete flag variety of isotropic subspaces of a four dimensional complex vector space with respect to a skew/symmetric form, and show that it is a singular del Pezzo surface of degree four.

We show that a weighted homogeneous complex surface singularity is metrically conical (i.e., bi-Lipschitz equivalent to a metric cone) only if its two lowest weights are equal. We also give an example of a pair of weighted homogeneous…

We show that smooth varieties of general type which are well formed weighted complete intersections of Cartier divisors have maximal Hodge level, that is, their the rightmost middle Hodge numbers do not vanish. We show that this does not…

We compute Hoelder Complexes,i.e. the complete bi-Lipschitz invariants, for germs of real weighed homogeneous algebraic or semialgebraic surfaces.

We prove that codimension two surfaces satisfying a nonlinear curvature condition depending on normal curvature are smoothly deformed by mean curvature flow to round points.

We investigate the characteristic numbers of Del Pezzo surfaces using degenerations.

We give a complete classification of Riemannian and Lorentzian surfaces of arbitrary codimension in a pseudo-sphere whose pseudo-spherical Gauss maps are of 1-type or, in particular, harmonic. In some cases a concrete global classification…

We classify del Pezzo surfaces with Picard number is equal to one and with four log terminal singular points.

We study del Pezzo varieties, higher-dimensional analogues of del Pezzo surfaces. In particular, we introduce ADE classification of del Pezzo varieties, show that in type A the dimension of non-conical del Pezzo varieties is bounded by $12…

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 construct a Kawamata type semiorthogondal decomposition for the bounded derived category of coherent sheaves of nodal quintic del Pezzo threefolds, decomposing the bounded derived category into bounded derived categories of finite…

The Fermi surface of the Bi2212 system is systematically studied using a variety of photon energies. In addition to reconciling the conflicting reports on the Fermi surface of this important material, we identify almost perfectly nested…

The Del Pezzo surface S\_6 obtained by blowing up the projective plane along three points (non aligned) has the following nice property : its osculating hyperplanes have a common point. For that reason S\_6 is also called Togliatti surface.…

Totally real surfaces in the nearly K\"ahler $\mathbb{C}P^3$ are investigated and are completely classified under various additional assumptions, resulting in multiple new examples. Among others, the classification includes totally real…

For every integer $a \geq 2$, we relate the K-stability of hypersurfaces in the weighted projective space $\mathbb{P}(1,1,a,a)$ of degree $2a$ with the GIT stability of binary forms of degree $2a$. Moreover, we prove that such a…