Related papers: On large theta-characteristics with prescribed van…

This paper contains results on stable bundles of rank 2 with space of sections of dimension 4 on a smooth irreducible projective algebraic curve $C$. There is a known lower bound on the degree for the existence of such bundles; the main…

Let P^2_r be the projective plane blown up at r generic points. Denote by E_0,E_1,...,E_r the strict transform of a generic straight line on P^2 and the exceptional divisors of the blown-up points on P^2_r respectively. We consider the…

If C is a curve of genus 4 without vanishing theta-nulls then there exists a unique (irreducible) Heisenberg-invariant quartic Q_C in |2\Theta| = P^{15} such that Sing Q_C contains the image of SU_C(2), the moduli space of rank 2 vector…

Let $X_0$ be an irreducible smooth projective curve defined over $\overline{\mathbb Q}$ and $f_0 : X_0 \rightarrow \mathbb{P}^1_{\overline{\mathbb Q}}$ a nonconstant morphism whose branch locus is contained in the subset $\{0,1, \infty\}…

Let $G$ be a simply connected semisimple algebraic group over $\mathbb{C}$ and let $\rho :G\rightarrow GL(V_\lambda)$ be an irreducible representation of highest weight $\lambda$. Suppose that $\rho$ has finite kernel. Springer defined…

We show that a general canonical curve is uniquely determined by the finite set of hyperplanes cutting theta-characteristics on it. Geometrical and combinatorial properties of the moduli space of stable spin curves are proved, which play an…

We study the variety of rank $\leq k$ quadrics containing a general projective curve and show that it has the expected dimension in the range $g-d+r\leq 1$. By considering the loci where this expectation is not true, we construct new…

The purpose of this note is to prove that there is an algebraic stack U parameterizing all curves. The curves that appear in the algebraic stack U are allowed to be arbitrarily singular, non-reduced, disconnected, and reducible. We also…

Let $C$ be a curve with two smooth components and a single node. Let $\mathcal{U}_C(r,w,\chi)$ be the moduli space of $w$-semistable classes of depth one sheaves on $C$ having rank $r$ on both components and Euler characteristic $\chi$. In…

Let $\mathcal{I}_{d,g,r}$ be the union of irreducible components of the Hilbert scheme whose general points correspond to smooth irreducible non-degenerate curves of degree $d$ and genus $g$ in $\mathbb{P}^r$. We use families of curves on…

An orthogonal bundle over a curve has an isotropic Segre invariant determined by the maximal degree of a Lagrangian subbundle. This invariant, and the induced stratifications on moduli spaces of orthogonal bundles, were studied for bundles…

We exhibit a class of "relatively curved" $\vec{\gamma}(t) := (\gamma_1(t),\dots,\gamma_n(t))$, so that the pertaining multi-linear maximal function satisfies the sharp range of H\"{o}lder exponents, \[ \left\| \sup_{r > 0} \ \frac{1}{r}…

We extend the results of Pareschi on the constancy of the gonality and Clifford index of smooth curves in a complete linear system on Del Pezzo surfaces of degrees $\geq 2$ to the case of Del Pezzo surfaces of degree 1, where we explicitly…

Let SU_C(2) denote the moduli variety of rank 2 semistable vector bundles with trivial determinant on an algebraic curve C. We prove that if C is trigonal then there exists a projective moduli variety N_C containing SU_C(2) as a subvariety…

Let C be a smooth complex projective curve of genus at least 2 and let M be the moduli space of rank 2, stable vector bundles on C, with fixed determinant of degree 1. For any k>1, we find two irreducible components of the space of rational…

We classify algebraic curves in $\mathbb{CP}^{n}$ ($n \geq 2$) that are invariant under an infinite subgroup of $\operatorname{PGL}(n+1,\mathbb{C})$. In particular, we prove that any irreducible, non-degenerate, one-dimensional algebraic…

In this article we explicitly compute the number of maximal subbundles of rank $k$ of a generically stable bundle of rank $r$ and degree $d$ over a smooth projective curve $C$ of genus $g\ge 2$ over $\C$, when the dimension of the quot…

We consider characterizations of projective varieties in terms of their tangents. S. Mori established the characterization of projective spaces in arbitrary characteristic by ampleness of tangent bundles. J. Wahl characterized projective…

We prove uniruledness of some moduli spaces $\bar{M}_{g,n}$ of stable curves of genus $g$ with $n$ marked points using linear systems on nonsingular projective surfaces containing the general curve of genus $g$. Precisely we show that…

We define and study the stack ${\mathcal U}^{ns,a}_{g,g}$ of (possibly singular) projective curves of arithmetic genus g with g smooth marked points forming an ample non-special divisor. We define an explicit closed embedding of a natural…