Related papers: On real forms of Fermat hypersurfaces

It is proven that for any topological or analytical types of isolated singular points of plane curves, there exists a non-real irreducible plane algebraic curve of degree $d$ which goes through $d^2$ real distinct points and has imaginary…

This paper intends to give a mathematical explanation for results on the zeta-function of some families of varieties recently obtained in the context of Mirror Symmetry. In doing so, we obtain concrete and explicit examples for some results…

We determine the finite groups whose real irreducible representations have different degrees.

We find the first examples of real hypersurfaces with two nonconstant principal curvatures in complex projective and hyperbolic planes, and we classify them. It turns out that each such hypersurface is foliated by equidistant Lagrangian…

We classify all real hypersurfaces with constant principal curvatures in the complex hyperbolic plane.

We determine the number of Del Pezzo surfaces of degree 2 over finite fields of odd characteristic with specified action of the Frobenius endomorphism, i.e. we solve the "quantitative inverse Galois problem". As applications we determine…

We study real elliptic surfaces and trigonal curves (over a base of an arbitrary genus) and their equivariant deformations. We calculate the real Tate-Shafarevich group and reduce the deformation classification to the combinatorics of a…

We provide explicit equations of some smooth complex quartic surfaces with many lines, including all 10 quartics with more than 52 lines. We study the relation between linear automorphisms and some configurations of lines such as twin lines…

In this paper, we use some basic quasi-topos theory to study two functors: one adding infinitesimals of Fermat reals to diffeological spaces (which generalize smooth manifolds including singular spaces and infinite dimensional spaces), and…

We present results expressing conditions for the existence of meromorphic first integrals for Pfaff equations of arbitrary codimension, integrable or not, on complex manifolds. These results are in the same vein as previous ones by J-P.…

We provide a resultant-based formula for the total degree w.r.t. the spatial variables of the generic offset to a parametric surface. The parametrization of the surface is not assumed to be proper.

We study the algebraic Brauer classes on open del Pezzo surfaces of degree $4$. I.e., on the complements of geometrically irreducible hyperplane sections of del Pezzo surfaces of degree $4$. We show that the $2$-torsion part is generated by…

We calculate the two-point Green's functions of operators dual to fermions of maximal gauged supergravity in four and five dimensions, in finite temperature backgrounds with finite charge density. The numerical method used in these…

We survey some results on real rational surfaces focused on their topology and their birational geometry.

For real irreducible algebraic curves of the seventh degree, there are 22 types of singular points of multiplicity six, 174 types of singular points of multiplicity five, and at least 182 types of singular points of multiplicity four. For…

We study and classify linearly normal surfaces in $\mathbf{P}^n$, of degree $d$ and sectional genus $g$, such that $d\geq 2g-1$.

We give an expression for number of points for the family of Dwork K3 surfaces $$X_{\lambda}^4: \hspace{.1in} x_1^4+x_2^4+x_3^4+x_4^4=4\lambda x_1x_2x_3x_4$$ over finite fields of order $q\equiv 1\pmod 4$ in terms of Greene's finite field…

We show that quasi-$F$-pure but not $F$-pure isolated quasi-homogeneous hypersurface singularities necessarily have $F$-pure threshold $1 - \frac{1}{p}$. This extends work of Bhatt and Singh beyond the Calabi-Yau case. We also classify the…

In this paper, we classify the Hopf hypersurfaces of the complex quadric $Q^m=SO_{m+2}/(SO_2SO_m)$ ($m\geq3$) with at most five distinct constant principal curvatures. We also classify the Hopf hypersurfaces of $Q^m$ ($m=3,4,5$) with…

We construct explicit families of quasi-hyperbolic and hyperbolic surfaces. This is based on earlier work of Vojta, and the recent expansion and generalization of it by the first author. In this paper we further extend it to the singular…