We investigate the intersection between the generalized quadrangle arising from a Hermitian surface H(3, q<sup>2</sup>) and an elliptic quadric Q<sup>-</sup>(3, q<sup>2</sup>) of PG(3, q<sup>2</sup>). In odd characteristic we determine the possible intersection sizes between H(3, q<sup>2</sup>) and Q<sup>-</sup>(3, q<sup>2</sup>) under the hypothesis that they share the same tangent plane at a common point. When the characteristic is even, we determine the configuration arising from the intersection of H(3, q<sup>2</sup>) and Q<sup>-</sup>(3, q<sup>2</sup>), provided that the generators of H(3, q<sup>2</sup>) that are tangents with respect to Q<sup>-</sup>(3, q<sup>2</sup>) are the extended lines of a symplectic generalized quadrangle W(3, q) embedded in H(3, q<sup>2</sup>). As a by-product, new infinite families of hyperovals on H(3, q<sup>2</sup>) are constructed.
On the intersection of a Hermitian surface with an elliptic quadric / Cossidente, Antonio; Pavese, Francesco. - In: ADVANCES IN GEOMETRY. - ISSN 1615-715X. - 15:2(2015), pp. 233-239. [10.1515/advgeom-2015-0006]
On the intersection of a Hermitian surface with an elliptic quadric
PAVESE, Francesco
2015-01-01
Abstract
We investigate the intersection between the generalized quadrangle arising from a Hermitian surface H(3, q2) and an elliptic quadric Q-(3, q2) of PG(3, q2). In odd characteristic we determine the possible intersection sizes between H(3, q2) and Q-(3, q2) under the hypothesis that they share the same tangent plane at a common point. When the characteristic is even, we determine the configuration arising from the intersection of H(3, q2) and Q-(3, q2), provided that the generators of H(3, q2) that are tangents with respect to Q-(3, q2) are the extended lines of a symplectic generalized quadrangle W(3, q) embedded in H(3, q2). As a by-product, new infinite families of hyperovals on H(3, q2) are constructed.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
