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This is a survey on the Fano schemes of linear spaces, conics, rational curves, and curves of higher genera in smooth projective hypersurfaces, complete intersections, Fano threefolds, etc.
Computation of parallel lines (envelopes) to parabolas, ellipses, and hyperbolas is of importance in structure engineering and theory of mechanisms. Homogeneous polynomials that implicitly define parallel lines for the given offset to a conic are fou
We count the number of conics through two general points in complete intersections when this number is finite and give an application in terms of quasi-lines.
We present detailed pedagogical derivation of covariant derivative of fermions and some related expressions, including commutator of covariant derivatives and energy-momentum tensor of a free Dirac field. The text represents a part of the initial cha
We consider a locally free sheaf $F$ of dimension 2 on $P^2$. A conic $q$ on $P^2$ is called a jumping conic if the restriction of $F$ to $q$ is not the generic one. We prove that the set of jumping conics is the maximal determinantal variety of a sk
We review the approach to the standard model of particle interactions based on spectral noncommutative geometry. The paper is (nearly) self-contained and presents both the mathematical and phenomenological aspects. In particular the bosonic spectral