Dang Tuan Hiep

Bio: Dang Tuan Hiep is an academic researcher from Duy Tan University. The author has contributed to research in topics: Calabi–Yau manifold & Equivariant map. The author has an hindex of 2, co-authored 4 publications receiving 13 citations. Previous affiliations of Dang Tuan Hiep include National Taiwan University.

On the degree of Fano schemes of linear subspaces on hypersurfaces

Abstract: In this paper we propose and prove an explicit formula for computing the degree of Fano schemes of linear subspaces on general hypersurfaces. The method used here is based on the localization theorem and Bott's residue formula in equivariant intersection theory.

On the degree of Fano schemes of linear subspaces on hypersurfaces

Abstract: 2. Equivariant intersectiontheoryEdidin and Graham [5, 6] gave an algebraic construction to equivari-ant intersection theory. In this section, we review the basic notionsand results of this theory. Let Gbe a linear algebraic group and letX be a scheme of finite type over C endowed with a G-action. Forany non-negative integer i, we can find a representation V of Gto-gether with a dense open subset U ⊂ V on which Gacts freely andwhose complement has codimension larger than dimX−isuch that theprincipal bundle quotient U→ U/Gexists in the category of schemes(see [5, Lemma 9]). The diagonal action on X× U is then also free,which implies that under mild assumption, a principal bundle quotientX×U→ (X×U)/Gexists in the category of schemes (see [5, Propo-sition 23]). In what follows, we will tacitly assume that the scheme(X× U)/Gexists and denote it by X

Rational Curves on Calabi-Yau Threefolds: Verifying Mirror Symmetry Predictions

Abstract: In this paper, the numbers of rational curves on general complete intersection Calabi-Yau threefolds in complex projective spaces are computed up to degree six. The results are all in agreement with the predictions made from mirror symmetry.

Lines, conics, and all that

Abstract: 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.

On Fano Schemes of Complete Intersections

Abstract: We provide enumerative formulas for the degrees of varieties parameterizing hypersurfaces and complete intersections which contain projective subspaces and conics. Besides, we find all cases where the Fano scheme of the general complete intersection is irregular of dimension at least 2, and for the Fano surfaces we deduce formulas for their holomorphic Euler characteristic.

Numerical invariants of Fano schemes of linear subspaces on complete intersections

Abstract: The goal of this paper is to explore the genus and degree of the Fano scheme of linear subspaces on a complete intersection in a complex projective space. Firstly, suppose that the expected dimension of the Fano scheme is one, we prove a genus-degree formula. Secondly, we give a degree formula for the Fano scheme.