허석문 교수

We investigate the moduli spaces of stable sheaves on a smooth quadric surface with linear Hilbert bipolynomial in some special cases and describe their geometry in terms of the locally free resolution of the sheaves.

Abstract We classify all the embeddings of \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathbb {P}_n$\end{document} in a Grassmannian Gr (1, N ) such that the composition with the Plücker embedding is given by a linear system of cubics on \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathbb {P}_n$\end{document} . As a direct corollary, we prove that every vector bundle giving such an embedding, splits if n ⩾ 3. © 2011 WILEY‐VCH Ver

In this thesis we study the restriction map from the moduli space of semistable coherent sheaves on the projective plane to the moduli space of semistable vector bundles on a quartic curve on the plane and try to give geometric description of the Brill-Noether loci of the latter. Each Brill-Noether locus is observed to be dominated by the moduli spaces over the plane with the proper Chern classes. We use different tools in algebraic geometry such as Cremona transformations, stable pairs, punctua

We classify globally generated vector bundles on with small first Chern class, i.e. , . Our main method is to investigate the associated smooth curves to globally generated vector bundles via the Hartshorne–Serre correspondence.

Abstract We study locally Cohen–Macaulay curves of low degree in the Segre threefold <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:msup> <m:mi>ℙ</m:mi> <m:mn>1</m:mn> </m:msup> <m:mo>×</m:mo> <m:msup> <m:mi>ℙ</m:mi> <m:mn>1</m:mn> </m:msup> <m:mo>×</m:mo> <m:msup> <m:mi>ℙ</m:mi> <m:mn>1</m:mn> </m:msup> </m:mrow> </m:math> {\mathbb{P}^{1}\times\mathbb{P}^{1}\times\mathbb{P}^{1}} and investigate the irreducible and connected components, respectively, of the Hilbert scheme of t

Abstract We define the notion of generalized logarithmic sheaves on a smooth projective surface, associated to a pair consisting of a reduced curve and some fixed points on it. We then set up the study of the Torelli property in this setting, focusing mostly in the case of the blow-up of the projective plane on a reduced set of points and, in particular, in the case of the cubic surface. We also study the stability property of generalized logarithmic sheaves as well as carrying out the descripti

We prove that the moduli space of stable sheaves of rank 2 with a certain Chern classes on a smooth quadric $Q$ in $\PP_3$, is isomorphic to $\PP_3$. Using this identification, we give a new proof that a certain Brill-Noether locus on a non-hyperelliptic curve of genus 4, is isomorphic to the Donagi-Izadi cubic threefold.

We classify all the embeddings of $\mathbb{P}_n$ in a Grassmannian $Gr(1,N)$ such that the composition with Plücker embedding is given by a linear system of cubics on $\mathbb{P}_n$. As a corollary in the direction of the Hartshorne conjecture, we prove that every vector bundle giving such an embedding, splits if $n\geq 3$.

We show the dominance of the restriction map from a moduli space of stable sheaves on the projective plane to the Coble quartic. With the dominance and the interpretation of a stable sheaf on the plane in terms of the hyperplane arrangements, we expect to investigate the geometry of the Coble quartic.