Related papers: On fake linear cycles inside Fermat varieties

The Fermat type Calabi-Yau $n$-fold, denoted by $\mathscr{F}_n$, is the hypersurface of $\mathbb{P}^{n+1}$ defined by $\sum_{i=0}^{n+1}x_i^{n+2}=0$, which is the smooth fiber over the Fermat point $\psi=0$ of the Fermat pencil $$…

We extend non-emtpyness and irreducibility of Hassett divisors to the moduli spaces of $M$-polarizable cubic fourfolds for higher rank lattices $M$, which in turn provides a systematic approach for describing the irreducible components of…

We propose a non-Hermitian (NH) interface system formed between two NH nodal line semimetals driven by optical fields as a platform for generation and tailoring of higher-order van Hove singularities (VHS). Through an analytical analysis of…

We compute the class of the locus in M_g of curves having a pencil with two unspecified triple ramification points. This is the first example of a geometric divisor on M_g which is not the pull-back of a divisor on the moduli space of…

We show that special cycles generate a large part of the cohomology of locally symmetric spaces associated to orthogonal groups. We prove in particular that classes of totally geodesic submanifolds generate the cohomology groups of degree…

Haj\'os conjecture asserts that a simple Eulerian graph on n vertices can be decomposed into at most (n - 1)/2 cycles. The conjecture is only proved for graph classes in which every element contains vertices of degree 2 or 4. We develop new…

For any subfield K of the complex numbers which is not contained in an imaginary quadratic number field, we construct conjugate varieties whose algebras of K-rational (p,p)-classes are not isomorphic. This compares to the Hodge conjecture…

Let $(V,q)$ be a non-degenerate $n$-dimensional quadratic space over the rationals of real signature $(r,s)$. For every integer $1\leq k \leq \min\{r,n-2\}$ we construct classes in the cohomology of arithmetic subgroups of $\mathrm{O}(V)$…

This thesis intends to make a contribution to the theories of algebraic cycles and moduli spaces over the real numbers. In the study of the subvarieties of a projective algebraic variety, smooth over the field of real numbers, the cycle…

We prove that for every graph $H$ of maximum degree at most $3$ and for every positive integer $q$ there is a finite $f=f(H,q)$ such that every $K_f$-minor contains a subdivision of $H$ in which every edge is replaced by a path whose length…

A fake wedge is a diagram of spaces K <- A -> C whose double mapping cylinder is contractible. The terminology stems from the special case A = K v C with maps given by the projections. In this paper, we study the homotopy type of the moduli…

We show that on the Jacobian $(JC,\theta)$ of a smooth curve $C$ of genus $g$, any effective cycle in $JC$ with cohomology class $\theta^d/d!$ is a translate of $W_{g-d}(C)$ or $-W_{g-d}(C)$. We then use this result to prove that for…

Given a polarizable $\mathbb{Z}$-variation of Hodge structures $\mathbb{V}$ over a complex smooth quasi-projective base $S$, a classical result of Cattani, Deligne and Kaplan says that its Hodge locus (i.e. the locus where exceptional Hodge…

This paper gives an expository account of our experiments concerning relations between modular forms for congruence subgroups of SL(3,Z) and three dimensional Galois representations. The main new result presented here is a calculation of…

We formulate the "real integral Hodge conjecture", a version of the integral Hodge conjecture for real varieties, and raise the question of its validity for cycles of dimension 1 on uniruled and Calabi-Yau threefolds and on rationally…

The fermion gaps are classified into order gap or Mott gap depending on the presence/absence of the order parameter. We construct the holographic model of the Mott gap using the field that is supported by the density only without…

A fake quadric is a smooth projective surface that has the same rational cohomology as a smooth quadric surface but is not biholomorphic to one. We provide an explicit classification of all irreducible fake quadrics according to the…

Having the potential for performing quantum computation, topological superconductors have been generalized to the second-order case. The hybridization of different orders of topological superconductors is attractive because it facilitates…

Function field lattices are an interesting example of algebraically constructed lattices. Their minimum distance is bounded below by a function of the gonality of the underlying function field. Known explicit examples--coming mostly from…

Fock modules for multi-dimensional Virasoro algebras (non-central extensions of the diffeomorphism algebra vect(N)) have recently been reported. Using ideas from the antifield formalism, I construct new classes of lowest-energy modules, as…