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Let $X$ be a smooth surface and let $\varphi:X\to\mathbb{P}^N$, with $N\geq 4$, be a finitely ramified map which is birational onto its image $Y = \varphi(X)$, with $Y$ non-degenerate in $\mathbb{P}^N$. In this paper, we produce a lower bound for the length of the pinch scheme of a general linear projection of $Y$ to $\mathbb{P}^3.$ We then prove that the lower bound is realized if and only if $Y$ is a rational normal scroll.Comment: 12 page
Given a closed, oriented surface, possibly with boundary, and a mapping class, we obtain sharp lower...
Let $|L_g|$, be the genus $g$ du Val linear system on a Halphen surface $Y$ of index $k$. We prove t...
We study rational surfaces on very general Fano hypersurfaces in $\mathbb{P}^n$, with an eye toward ...
We prove that the topological type of a normal surface singularity $(X,0)$ provides finite bounds fo...
In this thesis, we present the author's joint research with Lei Song, published in \cite{RS}. We sho...
We prove the Manin-Peyre conjecture for the number of rational points of bounded height outside of a...
AbstractLet X be the surface obtained by blowing up general points p1,…,pn of the projective plane o...
AbstractWe exhibit a sharp Castelnuovo bound for the ith plurigenus of a smooth minimal surface of g...
Let $X$ be a del Pezzo surface of degree one over an algebraically closed field $k$, and let $K_X$ b...
It is shown that if $\gamma: [a,b] \to S^2$ is $C^3$ with $\det(\gamma, \gamma', \gamma'') \neq 0$, ...
In this note, we give an alternative proof of uniform boundedness of the number of integral points o...
We prove that any smooth cubic surface defined over any number field satisfies the lower bound predi...
We show that smooth curves in the same biliaison class on a hypersurface in $\mathbf{P}^3$ with ordi...
We undertake a systematic study of Lipschitz Normally Embedded normal complex surface germs. We prov...
AbstractThis article contains a modern proof of the fact that, given a surface in P3 of degree m, wh...
Given a closed, oriented surface, possibly with boundary, and a mapping class, we obtain sharp lower...
Let $|L_g|$, be the genus $g$ du Val linear system on a Halphen surface $Y$ of index $k$. We prove t...
We study rational surfaces on very general Fano hypersurfaces in $\mathbb{P}^n$, with an eye toward ...
We prove that the topological type of a normal surface singularity $(X,0)$ provides finite bounds fo...
In this thesis, we present the author's joint research with Lei Song, published in \cite{RS}. We sho...
We prove the Manin-Peyre conjecture for the number of rational points of bounded height outside of a...
AbstractLet X be the surface obtained by blowing up general points p1,…,pn of the projective plane o...
AbstractWe exhibit a sharp Castelnuovo bound for the ith plurigenus of a smooth minimal surface of g...
Let $X$ be a del Pezzo surface of degree one over an algebraically closed field $k$, and let $K_X$ b...
It is shown that if $\gamma: [a,b] \to S^2$ is $C^3$ with $\det(\gamma, \gamma', \gamma'') \neq 0$, ...
In this note, we give an alternative proof of uniform boundedness of the number of integral points o...
We prove that any smooth cubic surface defined over any number field satisfies the lower bound predi...
We show that smooth curves in the same biliaison class on a hypersurface in $\mathbf{P}^3$ with ordi...
We undertake a systematic study of Lipschitz Normally Embedded normal complex surface germs. We prov...
AbstractThis article contains a modern proof of the fact that, given a surface in P3 of degree m, wh...
Given a closed, oriented surface, possibly with boundary, and a mapping class, we obtain sharp lower...
Let $|L_g|$, be the genus $g$ du Val linear system on a Halphen surface $Y$ of index $k$. We prove t...
We study rational surfaces on very general Fano hypersurfaces in $\mathbb{P}^n$, with an eye toward ...
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